Reduplication of adverb in Adv. + V1 + Adv. + V2 structure...?
This is a form of reduplication. However, the general form of reduplication depends on the word.
轻拿轻放 means someone picks up an item, and puts it down. The emphasis is on the gentleness of the action.
You could replace the 拿 with something else, but the 放 also needs to be replaced with something that is related to your substitute word. You could say “他轻手轻脚地走进房间。” 轻手轻脚 means that the person is trying to be quiet (i.e. gentle) when he enters the room.
The reduplication as mentioned above is ABAC. It can also be ACBC, for example. 大吃特吃 means “to eat voraciously”; this time, “eating” is emphasised, while 大 and 特 are used to “show” how the food is devoured.