I'm having quite a bit of trouble with this problem. It seems easy, but I just can't seem to get the idea.

I'm able to calculate the vertical components of the forces by using the summation of forces in the y direction equal to zero. The horizantal components, i'm pretty sure I need to use summation of torques, but there are only two forces! The force from each hinge in the horizantal direction! How would I go about solving htis?

You are given the vertical components of the force the hinges exert on the door. To find the horizontal components, take each hinge as a pivot point and realize that the torques about that point must add to zero.