To find the value of c, we need to multiply out the expression on the left side of the equation and then compare it to the right side of the equation.

First, let's expand the left side of the equation:
(ax + 2y)(3x + by)
= ax(3x) + ax(by) + 2y(3x) + 2y(by)
= 3ax^2 + abxy + 6yx + 2by^2
= 3ax^2 + 7xy + 2by^2

Now, we can compare the expanded left side to the right side of the equation:
3ax^2 + 7xy + 2by^2 = cx^2 + 7xy + y^2

By comparing the coefficients of the x^2 term, xy term, and y^2 term, we can see that:
c = 3a
7 = 7
2b = 1

Therefore, c = 3a. Given the information provided, we cannot determine the specific value of c or a without additional information.