Choice C is the correct answer. For infinitely many solutions, one equation must be a multiple of the other.

Step 1: Notice that the first equation's coefficients are double the second's: $6x + 8y = 2(3x + 4y)$

Step 2: Divide the first equation by 2: $\frac{6x + 8y}{2} = \frac{24}{2}$$3x + 4y = 12$

Verification: With $c = 12$, the first equation is exactly double the second: $2(3x + 4y) = 2(12) = 24$ ✓

💡 Strategic Tip: Scaling coefficients by a factor requires scaling the constant by the same factor.

Choice A is incorrect because $c = 6$ would give parallel lines (no solution).

Choice B is incorrect because $c = 8$ would give parallel lines.

Choice D is incorrect because $c = 24$ would give parallel lines.