Finding DNA from Amino Acid sequence problem
Your approach to translate the AA sequence, codon by codon, was correct. This was a bit of a trick question because to recognize it, you had to read the sequence backwards.

UGG-CAA-GGT-CAC etc is read directly off of the 3'->5' strand of the circled answer, reading from right to left.

The bottom left is a red herring because it starts with a start codon, ATG, but reading beyond the start codon, the sequence wouldn't match.