You have two equations:
1st: \(1J=1N*1m\)
and
2nd: \(1V=\frac{1J}{1C}\)
from the second equation you can extract Joule:
\(1J=1V*1C\)
you compare right side of the equation above to the right side of the 1s equation:
\(1V*1C=1N*1m\)
then you devide both sides by 1C and by 1m and you get:
\(\frac{1V}{1m}=\frac{1N}{1C}\)
