Get the intercepts:

g(x) = -x²+x+6
g(0) = -0²+0+6
g(0) = 6

So the y-intercept is (0,6)

      g(x) = -x²+x+6
         0 = -x²+x+6
    x²-x-6 = 0
(x-3)(x+2) = 0
  x-3=0; x+2=0
    x=3;   x=-2

So the x intercepts are (3,0) and (-2,0)

Plot those points:




Get some more points:

 x| y
-3|-6
-1| 4
 1| 6
 2| 4
 4|-6



Edwin