Learn Spanish (Spain): Terminan de comer tranquilamente.

It comes from the adjective tranquilo (calm). To make an adverb ending in -mente (which works just like "-ly" in English), you take the feminine form of the adjective (tranquila) and add -mente. So, tranquila plus mente becomes tranquilamente (calmly).

Could we put tranquilamente somewhere else in the sentence?

It sounds best exactly where it is! Adverbs of manner like tranquilamente usually go right after the verb or verb phrase they describe. Since terminan de comer acts as a single block of meaning ("they finish eating"), the adverb goes at the very end to describe how the whole action is done.

Why do we need the word de between terminan and comer?

To say you "finish doing" something in Spanish, you must use the set phrase terminar de followed by another verb. Here, terminan de comer means "they finish eating." If you leave out the de, the sentence is grammatically incorrect!

Why does the Spanish sentence use comer (to eat) when the English translation says "eating"?

In English, we say "finish eating" with an "-ing" verb. However, after a preposition like de, Spanish always requires the infinitive (the unconjugated dictionary form) of the verb. That is why we use comer rather than a Spanish "-ing" equivalent.