ExplanationThe given equation \((4x - 2y)(6x + 3y) = 18\) can be simplified as follows.

Step 1: Note that \((4x - 2y) = 2(2x - y)\) and \((6x + 3y) = 3(2x + y)\), so the given equation can be rewritten as \((2)(2x - y)(3)(2x + y) = 18\).

Step 2: Dividing both sides of the rewritten equation by 6 gives \((2x - y)(2x + y) = 3.\)

Step 3: Multiplying out the left side of the equation in Step 2 gives \(4x^2 - y^2 = 3\).

Since Quantity B is \(4x^2 - y^2\), it follows that Quantity A is equal to 3. Since Quantity A is 6, the correct answer is

Choice A.

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Sandy

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