Well, in order to get that you had to do distributive property, distributive property is when you get the outside number next to the parenthesis and multiply it by the numbers or variable inside the parenthesis one by one. So if she was trying to explain how you got the answer you got then you would say you used the distributive property. Now the (-4x)2 would look like (-4x)(-4x) nad the (9)2 will look like (9)(9) that is why it results in 16x2+81. When you square something it means that you multiply the first number or variable or both times the same. That is why you got that answer. Now I am going to make clear that you r(-4x) changed from a negative to a postive because when you multiply a negative times a negative(or divide also) it results in a positve.
Hope I explained it enough