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3 left-parenthesis 2 x squared plus 4 right-parenthesis minus 4 left-parenthesis x minus 6 right-parenthesis

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To simplify the expression \( 3(2x^2 + 4) - 4(x - 6) \), follow these steps:

  1. Distribute \( 3 \) to the terms inside the first parentheses: \[ 3(2x^2) + 3(4) = 6x^2 + 12 \]

  2. Distribute \( -4 \) to the terms inside the second parentheses: \[ -4(x) + (-4)(-6) = -4x + 24 \]

  3. Now combine the results from steps 1 and 2: \[ 6x^2 + 12 - 4x + 24 \]

  4. Combine like terms:

    • The \( x^2 \) term: \( 6x^2 \)
    • The \( x \) term: \( -4x \)
    • The constant terms: \( 12 + 24 = 36 \)

Thus, the expression simplifies to: \[ 6x^2 - 4x + 36 \]

This is the final simplified expression.