You can solve this problem the same way that you solve most problems with compound optical systems in simple geometrical optics, that is:
- Find the image(s) produced by the first element in the system
- Use those images as the objects for the next element in the system, find the resulting images.
- Repeat step 2 as neccesary.
In this case, there is a complication due to the fact that you essentialy have two paths in parallel to keep track of. More explicitly, find the images in each of the mirrors. Next, using those images as objects, find their images in the other mirrors. You will see that due to the geometry, at a certain point, you will run out of objects, because there are no more images generated in front of a mirror.
See also http://www.physicsclassroom.com/class/refln/u13l2f.cfm for some helpful diagrams and pictures.