Choice C is the correct answer. Let's check the relationship.

Step 1: Multiply the first equation by 2: $2(2x - 3y) = 2(6)$$4x - 6y = 12$

This is exactly the second equation!

Step 2: Since both equations represent the same line, they are identical (coincident).

This means infinitely many solutions—every point on the line satisfies both equations.

💡 Strategic Tip: Identical lines are a special case of "infinitely many solutions."

Choice A is incorrect because intersecting at one point requires different slopes.

Choice B is incorrect because perpendicular lines have slopes whose product is $-1$. Here, both have slope $\frac{2}{3}$.

Choice D is incorrect because the lines are not just parallel—they're the same line.