The line with equation $y=2 x-6$ has slope 2. When this line is translated, the slope does not change. The line with equation $y=2 x-6$ has $y$-intercept -6. When this line is translated upwards by 4 units, its $y$-intercept is translated upwards by 4 units and so becomes -2. This means that the new line has equation $y=2 x-2$. To find its $x$-intercept, we set $y=0$ to obtain $0=2 x-2$ and so $2 x=2$ or $x=1$. Thus, the $x$-intercept is 1.