On the assumption that you need to use threads in your solution, here's an idea.

Break the problem up so that you present a stream of partial solutions to a shared queue. Multiple threads can pick partial solutions off of the queue, and determine if the partial solution is in fact a complete solution.

As a partial solution, solve a simpler problem: pretend that Queens move only horizontally or vertically. Add all solutions to this simplified problem to shared queue. The (more computationally expensive?) step of determining if these solutions hold when Queens are allowed to move diagonally can be done in parallel (i.e., by multiple threads).