"What if you gave them more time?"
Translation:Et si tu leur donnais plus de temps ?
You have three mistakes in your sentence:
si + hypothetical clause calls for the imperfect (like in English: "what if you had..." as opposed to "of what if you give..."):
Et si tu avais donné...
object pronouns are always placed before the conjugated verb (the auxiliary verb in this case), except in the imperative:
Et si tu leur avais...
leur is not the direct object, but the indirect object (the direct object is "plus de temps"), so donné does not agree with it:
Et si tu leur avais donné plus de temps ?
Also, this sentence means "What if you had given them more time?" which means you cannot give them more time anymore, but you're wondering what happened if you had.
But I think English allows to use 'if you gave' instead of 'if you had given', so maybe it can be accepted.