It is not entirely explicit in the problem statement, but what is asked for is the maximum weight the crate may have, without breaking the ropes. We have three force vectors that point along pieces of rope: BA, BC, BD. Any of these forces is obviously proportional to the weight of the crate...
This is a rather simple problem. You get the force along AB from the weight of the crate. Then consider the relationship between the forces along AB and CB. Tip: Imagine the wheel's axle as fixed. The angle ABC can be read off directly from the diagram. With these, you can calculate the vector...