we know that
the x-intercept is when y=0 and z=0
-3x + 5y - 2z =60------------> -3x=60----------> x=-20
the point (-20,0,0)
the y-intercept is when x=0 and z=0
-3x + 5y - 2z =60------------> 5y=60----------> y=12
the point (0,12,0)
the z-intercept is when y=0 and x=0
-3x + 5y - 2z =60------------> -2z=60----------> z=-30
the point (0,0,-30)
the answer is
(-20,0,0)
(0,12,0)
(0,0,-30)