The best response function of firm 1 is b1(y2) = (90 y2)/2 (see example) and the best response function of firm 2 is
b2(y1) = (120 y1)/4 (see example).
Thus the Nash equilibria are the solutions of the equations
y1 = (90 y2)/2 y2 = (120 y1)/4.
These equilibria have a single solution, (y1, y2) = (240/7, 150/7). Thus the game has a unique Nash equilibrium, (y1, y2) = (240/7, 150/7).