Are you sure the problem says "sum" of and b? If it does then don't think the problem can be solved (and you will have to re-post it). But if it says "product" or "a*b" then keep reading...
The quickest way to figure out what the product of a and b must be is to use determinants. The determinant of the coefficients:
| a 2 |
| 3 b |
... will be zero if there are an infinite number of solutions.
If you do not know about determinants then we can try solving the system:
ax + 2y = 6k
3x + by = 15
Multiplying both sides of the first equation by -3 and both sides of the second equation by "a", we get:
-3ax + -6y = -18k
3ax + aby = 15a
The x terms cancel when we add the equations leaving:
-6y + aby = -18k + 15a
Factoring out y we get:
(-6 + ab)y = -18k + 15a
The x terms have already canceled out. When a system has an infinite number of solutions, then both the x's and the y's cancel out at the same time! So (-6 + ab) must be zero:
(-6 + ab) = 0
ab = 6
So there will be an infinite number of solutions if the product of a and b is 6. (You should get 6 if you used determinants, too.)