The largest 3-digit number x satisfying the congruence $$3x + 2 \equiv 4 (mod  13)$$ is

We need a three digit number which is of the form 3x + 2 and when this number is divided by 13, the remainder must be 4.
The largest 3 digit number of this form can be when x = 332 and the number comes out to be 998. When divided by 13, the remainder is not 4.
The next can be when x = 331 which makes the number as 995. When divided by by 13, remainder is not 4. 
The next can be x = 330 which makes the number as 992. When divided by by 13, remainder is 4. 

Hence, answer is 992. 
Another approach can be directly taking options from largest to smallest and actually dividing by 13 to arrive at the answer.