Ah, good question.

Насколько сильно - To what extent + strong~ how strongly...
Лондон нужен - is London needed
Вашингтону Трампа - Trump's Washington [Notice Трамп is his name's nominative, so the genitive, meaning -'s in this case, adds the usual а] [dative у on Washington]

How much does Trump's Washington need London?

This sentence does have multiple moving parts. I'd recommend, whenever you see a sentence with нужен(-на, -но) in it, start from that word, find the word that "is needed", then look for a dative. Since it is an adjective in the short form, we know it will be the star role in the sentence, and everything else will fall in around it; in most sentences, the verb would take this role.