There are two ways you can solve this problem, one is straightforward, but longer, while the other utilizes a trick and uses practically no work at all.
The first method for solving this problem is to break up the structure into 4 rectangles and then find their center of masses, and then use these positions, weighted with their respective areas, to find the center of mass (COM) for the entire structure:
Weighting each center of mass with its area we find:
The alternative solution is a bit more tricky. Find the center of mass of structure as if there were no hole in it, then find the COM of the hole, and subrtact it off from the solid rectangle weighting their areas:
