What is the duality of body and external name-and-form?

When there is a stand, a body (in sense of compound, not physical, see DD's answer in this regard), not-knowing, there is a surface, hence "duality".

By absence, having uprooted not-knowing, not dwelling on another stand, there is what goes beyond able to trace and discriminate. Others then the Nihilists idea, there "is" something beyond the six senses.

dvaya is just another word for avijja, not-knowing. Althought many try to trace something special, the Buddha used different words to serve different inclinatiins of different people.

[This answer is not given as means of trade, exchange, for Buddh-ism or other low wordily bonds but for liberations purpose]

1. "Sukhadukkhaṃ paṭisaṃvedayati" means "experience happiness & suffering" rather than "pleasant & painful feelings" (similar to how these words are used in MN 149), as follows:

And they experience physical and mental suffering. So kāyadukkhampi cetodukkhampi paṭisaṃvedeti

And they experience physical and mental pleasure. So kāyasukhampi cetosukhampi paṭisaṃvedeti.

2. "Kaya" means "collection" or "group" of five aggregates rather than "(physical) body".

3. There is no such thing as "external name-and-form" that together with a "kaya" creates contact. For example, "naming" is an internal process therefore external names (within the minds of others) cannot produce sense contact.

4. "Nama-rupa" here means "external minds & bodies". Thus with this internal collection ("kaya") of five aggregates plus external minds & bodies ("bahiddhā namarupa") there arises sense contacts that lead to producing (samudāgato) happiness & suffering.

5. For example, this internal collection ("kaya") of five aggregates has sense contact with an angry mind & body (nama-rupa) externally. Hindered by ignorance and fettered by craving, this internal collection of five aggregates ("kaya") creates the idea from the external mind & body of "my enemy"; thus generating suffering.

6. In summary, the beginning of SN 12.19 should be regarded the same as the following verse from SN 12.81:

At Sāvatthī. Then Venerable Rāhula went up to the Buddha, bowed, sat down to one side, and said to him: “Sir, how does one know and see so that there’s no ego, possessiveness, or underlying tendency to conceit for this conscious body and all external stimuli?” “Rāhula, one truly sees any kind of form at all—past, future, or present; internal or external; coarse or fine; inferior or superior; far or near: all form—with right understanding: ‘This is not mine, I am not this, this is not my self.’ One truly sees any kind of feeling … perception … choices … consciousness at all—past, future, or present; internal or external; coarse or fine; inferior or superior; far or near: all consciousness—with right understanding: ‘This is not mine, I am not this, this is not my self.’ That’s how to know and see so that there’s no ego, possessiveness, or underlying tendency to conceit for this conscious body and all external stimuli.”

External nama-rupa is external stimuli. However, there is no such thing as an "external name" that can be a stimuli. This is why the Pali term "nama" means "mind". External minds can be perceived and produced into suffering but external "names" cannot be perceived (unless they are spoken as words).

"Nama-rupa" comes from Brahmanism. The Buddha took this term and redefined it so it accords with suffering & the cessation of suffering (rather than according with the creationist philosophy of Brahmanism of 'naming-forms').

When ignorance & sankhara arise, they subject the mind-body to tension; just like an addiction causes the mind & body to seek out external sense contacts of sense gratification. Every translator that translates "nama-rupa" as "name-form" is wrong. Believe it or not!

The introduction of Balapandita Sutta (SN 12.19) is about person, the foolish and the astute, but the dependent origination is about five aggregates cycle, so the Buddha has to transform the person to be five aggregates for driving the cycle of aggregates in the depedent origination because there is no person in the dependent origination.

So there is the duality of this foolish body (person which referring to internal sense-field aggregates) and external name and form (aggregates which referring to external sense-field aggregates). Contact depends on this duality (those both internal and external sense-fields). When contacted through one or other of the six sense fields, the fool experiences pleasure and pain.

Iti ayañceva (bālo) kāyo (puggalo, paññatti) bahiddhā ca nāmarūpaṃ (khandho, paramattha), itthetaṃ dvayaṃ (ajjhatta&bahidhā-āyatanāni), dvayaṃ paṭicca phasso saḷevāyatanāni, yehi phuṭṭho bālo sukhadukkhaṃ paṭisaṃvedayati etesaṃ vā aññatarena.

You can use above explanation in various sutta depend on its context such as in DN22 MahasatipaṭṭhānaSutta:

ajjhatta-bahiddhā vā kāye kāyānupassī viharati

he dwells observing kāya in kāya internally and externally

The first kāya refers to a collection of 28 forms (the second kāya). Internal kaya is the practitioner's kāya and external kāya is the other's kāya.

See their Atthakathā for more information.

If the meaning is closer to the first translation; 'there is the twoness of this body and the external namarupam'

If so then the twoness is the name and the form (which are external or internal).

However i think the Tathagata is unlikely to use two words with same meaning in a sentence like that, it is my personal opinion and i just find it strange and out of character as i can't recall similar precedent.

Therefore i think the twoness could be a twofold statement about the body and the external namarupa being 'hindered by ignorance' and 'bound by craving'. So in this way it becomes a statement about the origination of the internal & the external existence in general.

Also kaya is probably the body, because later there is the somewhat common; 'with the breakup of the body..' and the breakup of the aggregates is not spoken of in that way afaik.

This is just an elaboration of D.O. Everything is clear and makes sense.

Delineation of feeling depends on the notion of contact.

Delineation of contact depends on separating totality into "internal" and "external".

Six sense doors are the subjective boundary across which the contact is made.

On this side of the boundary are upadana-skandhas - stuff we appropriate as I/mine.

On the other side of the boundary are the namarupas, the mind-made delineated entities that we designate as "external".

In each pair of DO, it's always a notion and its counterpart serving as foundation.