Upvote:3
It's possible, but you're not going to have a lot of time if you only have 6 hours to do it in, and I would not attempt this if you have a lot of bags to drag around.
Narita to Shibuya is about 80 minutes by Narita Express, although beware that not all N'EX trains stop at Shibuya, meaning you may have a wait of up to 30 minutes. There are other options (bus, connecting trains, etc), but none are meaningfully faster.
From Shibuya to Haneda, there are at least three different ways:
I'd allocate at least 3 hours in travel time alone. Add in one hour at Narita for immigration etc and another at Haneda for check-in etc (are you flying domestic or int'l?), and that leaves you with around one hour actually in Shibuya.