Answer
$$x = 1$$
Work Step by Step
We have $$y = 4(x+1) - 3x - (6-x)$$
To find the intercepts we need to make $y = 0$ and solve the equation for $x$ $$4(x+1) - 3x - (6-x) = 0$$
Doing all the multiplications in order to eliminate the parenthesis $$4(x) + 4(1) - 3x - 1(6) - 1(-x) = 0$$ $$4x + 4 - 3x - 6+x = 0$$
Taking all the $x$ terms to the left side of the equation and all the numbers to the right side $$4x-3x+x = 6 -4$$
Simplifying $$2x = 2$$
So the x-intercept is $$x = 1$$
