I am a multiple of 6 between 70 and 80. My ones digit is 6 when you remove 6.

Start skip counting by 6 until 6 x 6 so it will be within 70 - 80 when you multiply it again.

6 x 2 = 12

6 x 3 = 18

6 x 4 = 24

6 x 5 = 30

6 x 6 = 36

Now that we stopped, we multiply it by 2.

36 x 2 = 72

72 is within 70 - 80, so it is possible. Now let's check for other possible answers.

72 - 6 = 66, but it is not within 70 - 80, so cross it out.

72 + 6 = 78, so it is possible.

But how do we know if it is 72 or 78? Both are even because 6 is even. Now let's find out.

Well, my ones digit! Taken away from the ones digit, it becomes 70. But that's not a multiple of 6! And it is not within 70 - 80.

Well actually, we all get remainder 0 even when we divide them into 2, they are really even. Incase you thougt of it.

But when you remove six from it, let's try:

72 - 6 = 66, so it is possible.

78 - 6 = 72, so it is wrong.

The answer is 72.