6x^3/36x)*(49v^4/7v^2)

=[(6/36)*(x^3-1)]*[(49/7)*(v^4-2)]
=[(x^2)/6]*(7v^2)

=(7v^2x^2)/6 Is this the right answer? I feel like I missed something.

The constant coefficient should be 6*49/(7*36) = 7/6

The x exponent is 2 and the v exponent is 2.
=(7v^2*x^2)/6 is the correct answer.

However, some of the intermediate expressions you wrote, such as x^3-1, are ambiguous and could be misinterpreted.