The equation in the image is:

$2^{x+2} = \sqrt[3]{2}$

To solve for $x$, follow these steps:

1. Rewrite the cube root as an exponent: $\sqrt[3]{2} = 2^{\frac{1}{3}}$ Now, the equation is: $2^{x+2} = 2^{\frac{1}{3}}$

2. Since the bases are the same (both are base 2), you can set the exponents equal to each other: $x + 2 = \frac{1}{3}$

3. Solve for $x$ by subtracting 2 from both sides: $x = \frac{1}{3} - 2$

4. Simplify the right-hand side: $x = \frac{1}{3} - \frac{6}{3} = \frac{-5}{3}$ Therefore, $x = -\frac{5}{3}$.

The solution to the equation is $x = -\frac{5}{3}$.

Would you like more details or have any questions? Here are some related questions:

1. How do you simplify expressions involving cube roots?
2. What are some common methods to solve exponential equations?
3. Why do we equate exponents when the bases are the same?
4. How do you convert between radicals and fractional exponents?
5. Can logarithms be used to solve this problem?

Tip: When solving equations involving roots and exponents, converting everything to exponential form often makes the problem easier to handle.