We are tasked with finding the value of $4a + 2b$ when $a = 5$ and $b = -4$.

Step-by-step solution:

1. Start with the expression:
   $4a + 2b$

2. Substitute the given values for $a$ and $b$:
   $4(5) + 2(-4)$

3. Calculate each term:
   $4(5) = 20$
   $2(-4) = -8$

4. Add the results:
   $20 + (-8) = 12$

Thus, the value of $4a + 2b$ is $12$.

Would you like more details on any part of this solution?

Related Questions:

1. What is the value of $3a + 5b$ when $a = 2$ and $b = -3$?
2. How would the result change if $b = 3$ instead of $b = -4$?
3. Solve $6a + 7b$ for $a = -2$ and $b = 5$.
4. If $4a + 2b = 0$, what are the possible values of $a$ and $b$?
5. What is the value of $4(a + b)$ for $a = 1$ and $b = 2$?

Tip: Always substitute variables carefully into expressions to avoid sign errors when working with negative numbers.