Since the exponents are even, we can apply the property that,
If '$x$' is even $a^x – b^x$ is always divisible by $(a+b)$.
$6^256 - 4^256$ will always be divisible by $(6 + 4) = 10$.
Now any number multiplied by 10 gives the last digit as 'zero'.
The last digit of both the number are same as '6'
Thus after subtracting the unit's digit be '0'.