Sabina, before giving the answer, I would first explain you what are determiners.Determiners are the words that are prefixed or that come before a noun in a sentence to determine its' meaning. They can be articles - a, an,the; demonstratives- this, that, these, those;  possessives - my, your, our, his, her, its, their etc.

So, the answer to your query is "the" which makes the sentence:-

I gave him the books I had.

Hope this helps.