How many integers between 1 and 40 are multiples of 3 or 7?

Multiple means to self-add a number.

3: 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39
7 (excluding the same numbers): 7, 14, 28, 35.

Let's add up our numbers, since the question says "or".
We have 13 multiples of 3, and 4 multiples of 7.
13 + 4 = 17.

There is 17 numbers that are multiples of 3 or 7.

I hope this helps!