Please help me solve this bad boy!

No, you actually can solve it. You have to create two triangles, dividing the angle B in a 30 and 45 angle. Thus, you have a 30, 60, 90 triangle on the left, and a 45, 45, 90 triangle on the right. Then you can solve it. There you see that AC (I accidently wrote twice B) is equal to 2 root 2 +2 root 6