Remember this first.
The solution of an equation is the value or values that make the equation a true statement.
With this equation, we are looking for any value we can replace x with that will make the following equation true.
-2|x + 4| = 6
Start by dividing both sides by -2.
You get
|x + 4| = -3
The equation above states that if you take the absolute value of the sum of a a number and 4, you get -3. That is impossible because the absolute value of a number can never be negative.
If you take the absolute value of zero, you get zero. If you take the absolute value of a positive number, it's just the positive number. If you take the absolute value of a negative number, you get the opposite of that negative number, which is a positive number. An absolute value can only be positive or zero. It can never be negative.
No matter what number you choose for x, once you add that number to 4 and take the absolute value of the sum, you will never get a negative answer. Therefore, there is no value of x that will make this equation true. That is why there is no solution.