Let's solve the equation step by step:

Given: $3x + 2 = x + 4(x + 2)$

1. Expand the right-hand side: $3x + 2 = x + 4x + 8$

   Combine like terms: $3x + 2 = 5x + 8$

2. Move all terms involving $x$ to one side and constants to the other: $3x - 5x = 8 - 2$

   This simplifies to: $-2x = 6$

3. Divide by -2: $x = -3$

The solution is: $x = -3$

Would you like more details on the steps or have any questions?

Here are some related questions for further practice:

1. Solve $2x + 5 = 3(x + 1)$.
2. Solve $4x + 3 = 2x + 7$.
3. Solve $5x - 4 = 3(x + 2)$.
4. Solve $x + 2 = 4(2x - 1)$.
5. Solve $3x + 2 = 2(x + 3) + 1$.

Tip: When solving equations, always start by expanding and simplifying both sides as much as possible.