This is definitely one of those kinds of problems that's hard to do without visualizing the slab of wood.
Step one is to find the total area of the slab of wood before any cuts are made. What's the formula to find the area of a rectangle? base*height. The square is 18 long and 18 high, so to find the area you'd need to do 18*18, and you should get 324 inches^2 as the area of the square.
Step two is to find the area of a triangle. How can you find the area of a triangle? Well, think of it this way... What do you get when you cut a square in half, diagonally? A triangle! So if the formula for the area of a square is A=bh (base*height), then wouldn't the formula of a triangle be 1/2(bh), since a triangle is half of a square? Yep! So what would be the area of this triangle? It would be 1/2(6*4), because the base is 6 and the height is 4. 6*4 is 24, so now you have 1/2*24. One half of 24 is 12, so the area of the triangle he uses is 12.
Step 3: If he uses that wood, doesn't that mean he's taking it away? What's another word for "take away"? Subtract! That means you subtract the triangle he uses from the square he cut it out from! If the area of the square slab of wood is 324, and you subtract 12, 324 -12 is 312! That means that the area of wood he will have left over is 312 inches ^2! I hope this was helpful!