。
I have half as many books as he does.
Literal
I [to-は] his half [of-の] books only exist-not.
彼の半分 ('his half') uses 半分 as a noun to mean 'half [amount].' しか...ない ('only, nothing but [negative]') adds the exclusive limit. So 'only his-half's worth of books' = 'only half as many as he has.' The には in 僕には is again the target + contrastive — 'as for me specifically.'