Write the equation of the inverse of y = x-6

Y = (x - 6)/4

to find the inverse of a function, you swap the x and y variables, then solve for y.
y = (x - 6)/4 ... swap x and y
x = (y - 6)/4 ... solve for y, start by multiplying both sides by 4 to cancel out your denominator
4x = (y - 6) ... add 6 to both sides
4x + 6 = y

your inverse function is y = 4x + 6