y=x-32 and 3x=6+8y is another of writing the equations. So substitute y from the first equation into the second: 3x=6+8(x-32) to give us an equation in one variable only.
Therefore, 3x=6+8x-256, 256-6=8x-3x, 250=5x, so x=50 and y=50-32=18. This gives the point of intersection (x,y)=(50,18).
To find the angle between the lines, we need their slopes.
y=x-32, slope is 1 (ratio of the coefficients); 8y=3x-6, y=⅜x-¾, slope is ⅜.
The angles of the slopes are arctan(1)=45° and arctan(⅜)=arctan(.375)=20.56° approx. So the acute angle between the lines is 45-20.56=24.44° approx (angle of intersection).