Explanation:

In option 1 "A few judges have cut short their vacation to clear a long pending cases" "the" should be used instead of 'a' before the long pending cases because 'long pending cases' is plural.
In opiton 2 "A few judges have cut short vacation to clear the long pending cases" "their" should be used before the vacation.
In option 3 "A few judges has cut short its vacation to clear the long pending cases" 'have' should be used instead of 'has' because in the sentence 'Judges' is plural word.
Hence, option 4 is the correct answer.