What is the remainder of dividing by 9 the sum of the first two consecutive even numbers after 36?

Find what the first even number after 36 is equal to:

36 + 2 = 38.

We find what the second even number after 36 is equal to:

38 + 2 = 40.

We find what the sum of these two even numbers is equal to:

38 + 40 = 78.

We find what is the remainder of the division by 9 of the found sum:

78 = 72 + 7 = 9 * 7 + 7.

So the remainder of this sum divided by 9 is 7.

Answer: the required remainder of the division is 7.