Our first condition:
H × 6 gives the unit digit as H.
In the ones column, H can be 0, 2, 4, 6, or 8.
As H × 6 = H
If we consider the final product, then there is 1 at the hundreds place.
And this is only possible at G = 2.
When we multiply H with 6, carry over has to be 0. This means H = 0
Thus, G = 2, H = 0