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She couldn't think of what to give the kids for Christmas.
Literal
She [topic-は] Christmas [on-に] children [to-に] what [object-を] give-it-would-be-good [question-か] could-not-think-of.
An embedded wh-question: 何を与えたらいいか ('what would it be good to give') functions as the object of the main verb 思い付く. The pattern ~たらいいか is a standard frame for 'what should I do / what would be best' — literally 'if I do X, would it be good?' followed by the question marker か. 与える is the formal/literary verb 'to give,' more elevated than あげる and used when the giver is in a superior position (parents to children, gods to people, employers to staff). 思い付く ('think of, hit upon') in the negative past 思い付かなかった captures the moment of mental search ending in nothing — she searched, came up empty.