To factor the expression $3x^2 + 6x + 4x + 8$, we can proceed by grouping the terms.

1. Group the terms in pairs: $(3x^2 + 6x) + (4x + 8)$

2. Factor out the common factor from each group:

   • From $3x^2 + 6x$, factor out $3x$: $3x(x + 2)$
   • From $4x + 8$, factor out $4$: $4(x + 2)$

3. Now, notice that $x + 2$ is a common factor: $3x(x + 2) + 4(x + 2)$ This can be factored as: $(3x + 4)(x + 2)$

So, the factored form of $3x^2 + 6x + 4x + 8$ is $\boxed{(3x + 4)(x + 2)}$.

Would you like further details or have any questions?

Here are five related questions for further practice:

1. Factor the expression $2x^2 + 8x + 3x + 12$.
2. Factor $5x^2 + 15x + 2x + 6$.
3. Factor the quadratic expression $4x^2 + 16x + 4x + 16$.
4. What is the factored form of $7x^2 + 21x + 14x + 42$?
5. Factor $x^2 + 5x + 6$.

Tip: When factoring by grouping, always look for common factors within each group first, and then check if there's a common binomial factor to factor out.