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The simplified expression is \(6m^{5}\).
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To simplify the expression \( 12 m^{5} - 2 m^{2} \times 3 m^{3} \), we first perform the multiplication: \[ 2 m^{2} \times 3 m^{3} = 6 m^{5}. \] Now, we can substitute this back into the expression: \[ 12 m^{5} - 6 m^{5}. \] Next, we combine the like terms: \[ (12 - 6) m^{5} = 6 m^{5}. \] Thus, the fully simplified expression is \( 6 m^{5} \).