To find the \(x_i\) intercept, set \(x_j=x_k=0\). By this I refer to the following procedure.
x-intercept: Set \(y=z=0\), then you're left with \(4x=60\iff x=15\). Then the x-intercept is \((15,0,0)\).
y-intercept: Set \(x=z=0\), then \(-6y=60\iff y=-10\). The y-intercept is \((0,-10,0)\).
z-intercept: Set \(x=y=0\), then \(-5z=60\iff z=-12\). The z-intercept is \((0,0,-12)\).
