Ahins wrote:

Take an even number. If you multiply it by 4, then you get the number P. If you half it then you get the number Q. P-Q is always a multiple of seven.

For example, if we choose 10, then P=40 and Q=5. 40-5=35, which is a multiple of seven. Explain why regardless of which even number you start with, you will always get a multiple of seven.

This is a totally inappropriate 11+ question: which school is this?

Take a general even number 2n

P = 4 x 2n = 8n

Q = 2n divided by 2 = n

P - Q = 8n - n = 7n hence always a multiple of 7.