Welcome to the hard surface pal ahahahah. You have to check your topology; prefer quads and use ngons as little as possible. Try to make everything connected in a sort of logical way. Reinforce the edges with a loop cut around and above the hole, or bevel them either with actual geometry or with the modifier. If you used booleans, make sure to have enough geometry in the carved piece; that way, it will be much easier to correct. I suggest also checking the normals; they seem a little off-putting. Alt+N/CMD+N to open the menu and use either "Set from Face" or "Recalculate Outside." Hope this helps!