Math Help - I'm new and nned help with a theory prolem.

I'm taking a math theory class and am in over my head. I'm making it but am completely stumped by this question. "Jill asks each of her classmates to choose a number, then multiply the number by -3, add 2 to the product, multiply the result by -2, and then subtract 14. Finally, each student is asked to divide the result by 6 and record the answer. When Jill gets their answers, she adds 3 to it in her head and announces the number that classmate originally chose. How did Jill know to add 3 to ach answer?"

Can anyone help?

Let x be the number.
1)multiply by -3 ( -3x )
2)add 2 to the product ( -3x + 2 )
3)multiply the result by -2 ( -2*(-3x+2) = 6x - 4 )
4)subtract 14 ( 6x - 4 - 14 = 6x - 18 )
5)divide by 6 ( )
6)record the answer they give ( call it p) ( x - 3 = p )
7)x = p + 3