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The Rosary is a good example of doing mental and vocal prayer at the same time. You say the words of the Rosary while meditating on the mysteries and at the same time the words of the Rosary.
St. Louis DeMontfort's "Secret of the Rosary" is a good reference for getting the most of the prayers contained in the Rosary.
Usually, however, prayer isn't broken down into Mental vs Vocal - but
Meditative prayer is prayer where you may read
Contemplative prayer is a deeper form where God provides the direction. Ideally, someone progresses from Vocal to Meditative to Contemplative prayer (maybe never quite reaching contemplative prayer) but never abandoning one for the other because vocal prayer, like the Rosary, Mass and Liturgy of the Hours is prayed in common by the oldest monks and the smallest children and it is still for the benefit of their souls; it also will always have a meditative element to it (note the pauses).
There may be less opportunity for contemplation while vocal prayers are happening and for that, if you want to do it in communion, Eucharist Adoration is a great option.
https://www.usccb.org/catholic-prayers good resource on meditation and adoration
http://www.scborromeo.org/ccc/p4s1c3a1.htm#2723 Types of prayer in the Catechism