How do I turn x-y=6 into y=6-x

Simple answer, you cant

but to come close

x-y = 6

subtract x to both sides

x-y-x=6-x

-y=6-x

multiply negative 1 to both sides

(-1) - y = - 1 (6-x)

distribute the negative sign

y=-6+x

y=x-6

this is different from y=6-x which is why I said you cant