copper(II) oxide reacts with hydrogen gas. If this reaction takes place at SLC, what is the least amount of hydrogen gas needed to react with CuO. Mass of CuO=2.71g and mass of copper(product) is 2.17grams.

Well, you need a balanced equation first.

Then you can work out how many moles of copper you have as the end product, and therefore you can establish how many moles of H2 you must need. This seems to be enough to answer the question. Don't know why you were given information about SLC. (Well I do know why, but the question doesn't ask for it, at least how you have worded it.)

Let me know if you need further help.

CuO +H2--->Cu +H2O
I worked out the number of moles to be 0.034... so 0.0034 mol of H2 is needeD?

Erm, 0.034. Yes. Sounds right if everything else you've calculated is right.