Question

Find the numbers that each letter stands for. EFGHx4=HGFE
E=
F=
G=
H=

Answer 1

E must be 1 or 2 so than 4xEFGH can be a four-digit number. E must be 2 because multiplying EFGH by 4 would required that E be an even number.
H must therefore be 8 since E is 2.

Thus EFGH is 2--8 and HGFE is 8--2.
In order for HGFE to begin with 8, F must be 1 or 2. Let's try 1, since we have a 2 already.

Now we have 21_8 = 8_12

With only ten digits to try, it is easy to see that the numbers are 2178 and 8712