Question

Write an equation of the line passing through point $P\left(4,\ 0\right)$ that is parallel to the line $-x+2y\ =\ 12$

Answer 1

Good grief!!

Just type it like this:

Write an equation of the line passing through point P(4,0) that is parallel to the line -x + 2y = 12

The standard way would be to have the leading term as positive, so your
given equation is
x - 2y = -12

Your new equation will differ only in the constant, so
x - 2y = c
given: (4,0) lies on it, so
4 - 0 = c
c = 4

x - 2y = 4 is your new equation.