Find the smallest positive integer satisfying both of the following requirements:
$(a)$ Its units digit is $6$
$(b)$ If the units digit $6$ is moved before the first digit, the new number is $4$ times the original number.
Well obviously the units digit of the answer is $6$, but I don't know how to proceed. The only explanation I received was "Just work out the digits one by one, starting from the right," which to me is ambiguous.