Answer:

value of x is -2.

Step-by-step explanation:

the answer is correct

[tex]2 {}^{x + 4} - 2 {}^{x + 2} = 3 \\ \\ ( {2}^{4} \times {2}^{x} - {2}^{2} \times 2 {}^{x} ) = 3\\ \\(16 \times {2}^{x} - (4 \times {2}^{x} ) = 3 \\ \\ {2}^{x} (16 - 4) = 3 \\ \\ {2}^{x} (12) = 3 \\ \\ {2}^{x} = \frac{3}{12} \\ \\ {2}^{x} = \frac{1}{4} \\ \\ {2}^{x} = {2}^{ - 2} \\ \\ x = - 2[/tex]