15 works also (L= 5.186, W=2.314)
You are correct.
a) Area = 12 (no solution)
b) Area = 14 (L=3, W=4)
c) Area = 15 (L=2.32, W=5.19)
d) Area = 21 (L=1.30, W=9.19)
Note roles of L and W can be reversed, and answer (b) is the only one that yields integer side lengths, but that constraint was never specified, so c and d are valid answers also. Also the above values are approximate since I just eyeballed them off a graph.
They aren’t asking for area. They want the perimeter. So you have to have L*W=12 AND 2L+2W=one of the choices.