Subtract. \( \left(4 m^{3}+6\right)-\left(-2 m^{3}+m^{2}+3\right) \) \( 6 m^{3}+m^{2}+3 \) \( 6 m^{3}+5 m^{2}-3 \) \( 6 m^{3}-m^{2}+3 \) \( 2 m^{3}+m^{2}+9 \)

Let's perform the subtraction step by step: Given: \[ \left(4 m^{3} + 6\right) - \left(-2 m^{3} + m^{2} + 3\right) \] 1. **Distribute the negative sign:** \[ 4 m^{3} + 6 + 2 m^{3} - m^{2} - 3 \] 2. **Combine like terms:** - **\( m^{3} \) terms:** \( 4 m^{3} + 2 m^{3} = 6 m^{3} \) - **\( m^{2} \) terms:** \( -m^{2} \) (only one term) - **Constant terms:** \( 6 - 3 = 3 \) 3. **Write the simplified expression:** \[ 6 m^{3} - m^{2} + 3 \] **Therefore, the correct answer is:** \[ 6 m^{3} - m^{2} + 3 \]