You're given a point on each line, so you can substitute the coordinate values into their respective equations. For the first line:

y = 2x + b

r = 2p + b

For the second line:

y = 3x + b

3r = 3(4p) + b

3r = 12p + b

We now have a system of linear equations. When we have two equations that are not equivalent, we can solve for two variables; here, however, we have three variables — r, p, and b — so how can we solve? The key here is to recognize that though we have three variables, we don't need to solve for r or p; we just need to solve for a relationship between r and p, because the solve-for is r / p, not any individual values. If we can just get an equation with r and p as the only two variables, we can manipulate it to solve it for r / p, so the next move is to eliminate b; we can subtract one from the other to eliminate b:

  3r = 12p + b
-  r =  2p + b
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  2r = 10p

Now, we just need to solve for r / p; we do not need to solve individually for r or p:

2r = 10p

2r / p = 10

r / p = 10 / 2

r / p = 5