Each letter represents a unique number.
What number does each capital letter represent? ('x' is just the multiplication sign)

G D F E N
______x4_
N E F D G

G must be an even number since it is the result of multiplication by 4. If it were higher than 2, there would have to be 6 digits in the product. So G = 2.

Looking again at the product, N must be 8 or 9, but only 8 will give a product ending in 2 when multiplied by 4. So N = 8.

D can only be 1, since a higher number would give a product beginning with 9.

E must be 7, since 4 x 78 = 312.

That leaves 3, 5, 6 and 9 as possibilities for F, and 9 is the only one that fits.

So 21978 x 4 = 87912