2005 AMC 12B Problem 7

Setting $y = 0$ gives $|3x| = 12,$ so $x = \pm 4.$ Setting $x = 0$ gives $|4y| = 12,$ so $y = \pm 3.$ The graph is a rhombus with vertices $(\pm 4, 0)$ and $(0, \pm 3),$ so its diagonals have lengths $8$ and $6.$ Its area is $\dfrac12 \cdot 8 \cdot 6 = 24.$ Thus, the correct answer is D.