Solve 4∣𝑥+6∣=164∣x+6∣=16.

Sure, let's solve the equation step by step.

The given equation is 4|x+6| = 16.

Step 1: Divide both sides by 4 to isolate the absolute value. |x+6| = 16/4 |x+6| = 4

Step 2: Solve for x in the absolute value equation. An absolute value equation has two solutions.

So, x + 6 = 4 and x + 6 = -4

Step 3: Solve for x in both equations.

For x + 6 = 4, subtract 6 from both sides to get x = 4 - 6 = -2.

For x + 6 = -4, subtract 6 from both sides to get x = -4 - 6 = -10.

So, the solutions to the equation 4|x+6| = 16 are x = -2 and x = -10.