To find the value of a/c, we need to solve the given system of equations and determine the relationship between a and c. Let's start by analyzing the equations:

Equation 1: ax + 3y = c
Equation 2: 6x + 9y = 15

To solve this system, we can use the method of substitution or elimination. Let's use the method of substitution:

1. Solve Equation 2 for x:
6x = 15 - 9y
x = (15 - 9y)/6

2. Substitute the value of x in Equation 1:
a((15 - 9y)/6) + 3y = c
(15a - 9ay)/6 + 3y = c

3. Multiply through by 6 to eliminate the denominator:
15a - 9ay + 18y = 6c
15a - 9ay + 18y - 6c = 0

4. Rearrange the equation:
15a - 9ay + 18y - 6c = 0
15a - (9a - 18 + 6c)y = 0

5. Set the coefficient of y to zero:
9a - 18 + 6c = 0

6. Solve for a/c:
9a = 18 - 6c
a = (18 - 6c)/9
a/c = (18 - 6c)/(9c)

Now, we need to find the value of a/c when the system has infinitely many solutions. For a system to have infinitely many solutions, the two equations must represent the same line. This happens when the coefficients of x and y are proportional.

7. Set the coefficients of x and y proportional:
6/3 = (18 - 6c)/(9c)
2/1 = (18 - 6c)/(9c)

8. Cross-multiply and simplify:
2(9c) = (18 - 6c)(1)
18c = 18 - 6c

9. Combine like terms:
18c + 6c = 18
24c = 18

10. Solve for c:
c = 18/24
c = 3/4

11. Substitute the value of c back into the equation for a/c:
a/c = (18 - 6(3/4))/(9(3/4))
a/c = (18 - 9/2)/(27/4)
a/c = (36/2 - 9/2)/(27/4)
a/c = (27/2)/(27/4)
a/c = (27/2) * (4/27)
a/c = 2/2
a/c = 1

Therefore, the value of a/c when the system has infinitely many solutions is 1. The given answer of 2/5 is incorrect.