"Where can we put the cups?"
I think it sounds better if you move the object to the front: 杯子可以放在哪儿？ But I guess this sentence is about the use of 把?
It's a sentence structure for when the verb has a direct object and also some kind of complement after the verb. (You can't end this kind of sentence with the verb.)
"To put, or place"
https://en.wiktionary.org/wiki/把 A light verb or preposition placed before the object of a sentence to allow it to be placed before the verb, giving greater flexibility in complex sentence construction. 他把刀放在桌子上。 Tā bǎ dāo fàng zài zhuōzi shàng. He put the knife on the table.