The x and y intercepts are found by putting x=0 (y=-20) and y=0 (x=12) for the first line; and y=9 and x=8 for the second line. As for the fractions, they can be removed by multiplying the first eqn through by 15 (the LCM of 3 and 5) to give 5x-3y=60 and the 2nd eqn by 12 (LCM of 3 and 4) to give 9x+8y=72. The intercepts remain the same, proving that the graphs are unaffected by rewriting.
To find where they intersect we can use either form of the equations, but you will probably be happier with the more familiar form. Multiply the first of the rewritten eqns by 8 and the second by 3: 40x-24y=480 and 27x+24y=216. Now add these so that y is eliminated: 67x=696, so x=696/67. To find y, we can use 8y=72-9x=72-9*696/67, so y=-180/67. If these values are substituted in the original or rewritten equations they should both balance: 696/3*67+180/5*67=232/67+36/67=4; 3*696/4*67-2*180/3*67=6. So, despite its ugliness the point of intersection is (696/67,-180/67) or (10.388,-2.687) approx.
Fractions are just numbers so 5x and (1/3)x, for example, are still a number multiplied by x. But you can always remove fractions in an equation by multiplying by an integer into which the numerator(s) divide(s).