1. **State the problem:** Factorize the quadratic expression $2x^2 + 6x + 4$. 2. **Recall the factoring formula:** For a quadratic $ax^2 + bx + c$, we look for two numbers that multiply to $a \times c$ and add to $b$. 3. **Calculate product and sum:** Here, $a=2$, $b=6$, $c=4$. So, product = $2 \times 4 = 8$, sum = $6$. 4. **Find two numbers:** The numbers that multiply to $8$ and add to $6$ are $2$ and $4$. 5. **Rewrite the middle term:** $2x^2 + 2x + 4x + 4$. 6. **Group terms:** $(2x^2 + 2x) + (4x + 4)$. 7. **Factor each group:** $2x(x + 1) + 4(x + 1)$. 8. **Factor out common binomial:** $(2x + 4)(x + 1)$. 9. **Simplify further:** Factor out $2$ from $(2x + 4)$ to get $2(x + 2)(x + 1)$. **Final answer:** $$2(x + 2)(x + 1)$$