Which equation represents the same line as 2x + 3y = 12?

Two equations describe the same line when one is a nonzero multiple of the other. Multiplying every term of $2x + 3y = 12$ by 2 gives $4x + 6y = 24$, choice D. Choice A ($2x + 3y = 6$) keeps the same left side but changes the right side, so it is a parallel line. Choice B ($4x + 3y = 24$) doubles the $x$-coefficient and constant but not the $y$-coefficient, giving a different slope. Choice C ($2x - 3y = 12$) changes the sign of the $y$-term, so it has the opposite slope. All three share a point or direction but not the whole line.