Only the answer from the book is correct.
Since the sentence posits that the problems are real and not hypothetical, the default mood to use is the indicative. There would have to be an explicit reason (grammatical or otherwise) for a switch to the conditional, and there is none.
In German, using the conditional in the main clause ("Wenn ich wüsste" or "If I knew") is not a reason to switch from the indicative ("welche Probleme du hast" or "the problems you have") to the conditional ("welche Probleme du hättest" or "the problems you would have").
Indeed, the literal backtranslation of your suggested sentence is wrong in English as well:
*If I knew the problems you would have, I could help.
In English I believe the first of the following sentences is correct and the second one is not (correct me if I'm wrong), which implies that in English the conditional in the main clause leads to a switch from the present to the past tense:
If I knew the problems you had, I could help.
*If I knew the problems you have, I could help.
However, this switch in English is a grammar convention (the conditional expressed by the past tense requires the past tense in the secondary clause as well), and there is no similar convention in German.