Thank you for the opportunity to help you with your question!
In the original integral, the integration order is dydx. This integration order corresponds to integrating first with respect to y (i.e., summing along rows in the picture above), and afterwards integrating with respect to x (i.e., summing up the values for each row). Our task is to change the integration to be dxdy, which means integrating first with respect to x. Please let me know if you need any clarification. I'm always happy to answer your questions.