I'd like it vs. I'd like that?

I’m a native English speaker, and I’m trying to explain to my Russian friend what the difference is but I just can’t.

I asked her if she would like for me to send her some songs that could help improve her English (she already has a very advanced level) and she said "I’d like it!". I know that in this situation, "I’d like it!" doesn’t sound too bad, but it sounds a bit more unnatural to me than "I’d like that" would.

Any explanations?