Simplify the given mathematical expression: $2\left(3 x^{2}+5 x-9\right)-\left(x^{2}+2 x+6\right)$

Step 1 ：Distribute the 2 in the first parentheses: \(2*(3x^{2}+5x-9) = 6x^{2}+10x-18\)

Step 2 ：Subtract the second parentheses from the result: \(6x^{2}+10x-18 - (x^{2}+2x+6) = 5x^{2}+8x-24\)

Step 3 ：Final Answer: The simplified expression is \(\boxed{5x^{2} + 8x - 24}\)