With or without FOR? "The last thing I want is (FOR) anyone to..."
Solution 1:
No, your answer is plain wrong.
It would be correct to say “I don’t want anyone to intervene”. But in your example the clause “anyone to intervene” is a predicate to “thing”, not a complement to “want”.
Try slightly changing the word order: “For anyone to intervene is the last thing I want” is correct. “Anyone to intervene is the last thing I want” is obviously incorrect.