To solve the problem in the image:

The height of the rectangle is $3b^2$ and the width is given by $4b^4 + 2b - 6$.

To find the area of the rectangle, we need to multiply these two expressions together:

$\text{Area} = (3b^2) \times (4b^4 + 2b - 6)$

We'll distribute $3b^2$ to each term inside the parentheses:

1. $3b^2 \times 4b^4 = 12b^6$
2. $3b^2 \times 2b = 6b^3$
3. $3b^2 \times (-6) = -18b^2$

Now, combine these results:

$\text{Area} = 12b^6 + 6b^3 - 18b^2$

So, the area of the rectangle is:

$12b^6 + 6b^3 - 18b^2$

Would you like any more details or explanations?

Here are five related questions to help expand your understanding:

1. What is the process of distributing a term over a polynomial called?
2. How would the solution change if the rectangle's height was different, say $4b^2$?
3. Can you factor out any common terms from the expression $12b^6 + 6b^3 - 18b^2$?
4. How would you approach this problem if the rectangle's dimensions were given in more complex expressions?
5. What is the significance of expressing the area as a polynomial?

Tip: Always double-check your distribution to make sure every term inside the parentheses is multiplied correctly!