I don't have access to Matlab, so I cannot offer technical advice. But if I were doing the question I would avoid the use of a phase plot and would, instead, just write down the formula for the DE solution; it would be a formula that has both R and t in it: L = f(t,R). Then I would set L=0 at t=12 and solve the equation to find R.
I guess if you want to use phase plot methods you could start by guessing a value of R, then make the phase plot for that R value and trace out the solution. If L=0 occurs before t=12 our guessed value if R is too large, so we should decrease it a bit and start over. If L=0 occurs after t=12, our guessed R is too small, so we should increase it a bit and start over. This procedure would be horrible and would take forever, and that is why I would not use it unless I had hours of spare time and nothing better to do.