so first make it into slope intercept form y=mx+b
1/2x-3y=8
subtract 1/2x from both sides
-3y=8-1/2x
multiply both sides by -1
3y=1/2x-8
divide both sides by 3
y=1/6x-8/3
the x intercept is when y=0
so set y to zero
0=1/6x-8/3
add 8/3 to both sides
8/3=1/6x
multiply both sides by 6
16=x
the x intercept is 16