since 16 = 4^2, it should be (3w-4)^2. ^2 is square, not multiply, bear in mind.
He should have used cross method. 9w^2=3w*3w. 16=4*4. In order to get -24w, one of the numbers will have two negative numbers to make a positive, so 16=-4*-4.
square root of 16 is 4^2 hence when removing the brackets the result becomes (3w-4)^2
He should have transferred the 4 to the last line. Instead, he transferred it wrongly and put 8. I think he must have multiply the square with the 4.