I need help, can someone help me show how we get the solution as stated in the question; as i am trying my very best to solve.
Remember that you can break a object into pieces. The centroid of the whole object is the weighted centroids of the pieces. Since this is a planar object, the centroids of the pieces are weighted according to the area of those pieces.
Your object is regular enough so that it can be broken into pieces for which centroids can be easily found, like rectangles and triangles.