Determine the x-intercept of the function: 15. $f(x)=4-|6+2 x|$

Step 1 ：Set the function equal to zero: \(0 = 4 - |6 + 2x|\)

Step 2 ：Rewrite the equation: \(|6 + 2x| = 4\)

Step 3 ：This represents two equations: \(6 + 2x = 4\) and \(6 + 2x = -4\)

Step 4 ：Solve the first equation: \(6 + 2x = 4\), subtract 6 from both sides to get \(2x = -2\), then divide both sides by 2 to get \(x = -1\)

Step 5 ：Solve the second equation: \(6 + 2x = -4\), subtract 6 from both sides to get \(2x = -10\), then divide both sides by 2 to get \(x = -5\)

Step 6 ：The x-intercepts of the function \(f(x) = 4 - |6 + 2x|\) are \(\boxed{x = -1}\) and \(\boxed{x = -5}\)