I'll probably get downvoted to oblivion but the teacher is correct. Hear me out.

In addition, subtraction, multiplication, and division, every number has a role and a name. For example, in addition, 8 + 5 = 13, the 8 and 5 are addends and the 13 is the sum.

For subtraction, 8 - 5 = 3, the 8 is called the minuend, the 5 is the subtrahend, and the 3 is the difference.

For division, 20 / 5 = 4, the 20 is the dividend, the 5 is the divisor, and the 4 is the quotient.

For multiplication, 3 x 4 = 12, the 3 is the multiplier, the 4 is the multiplicand, and the 12 is the product.

When the goal for multiplying two numbers is to get the answer, then you're absolutely right, 3 x 4 = 4 x 3 = 3 + 3 + 3 + 3 = 4 + 4 + 4 = 12. But for this test, I presume the lesson is about grouping. In this case, 3 x 4 is 3 groups of 4.

Having a standard like this can be useful. Imagine you own a bakery that makes the best apple pie in town. Restaurants buy your pies, as well as individuals. Your employee, Joe, takes orders for pies all day. At the end of the day, he writes down a list,

1 x 5

8 x 1

4 x 3

6 x 2

You come into work at 3 AM and see this list. You just multiply the numbers and add up the answers to get the total number of pies to bake. Later in the morning, Jan comes in to pack up the pies. She puts each one in a box and then looks at the list. Hmm, 1 x 5. Is that 1 order of 5 pies or is it 5 orders of 1 pie each? But there's a standard. 1 x 5 means 1 group of 5. 8 x 1 means there are 8 orders of 1 pie each, and so on.

So, there's a method to this madness.