Let's solve the expression provided in the image:

$(4x^6 + 8x^3) - (7x^2 + 6x^3)$

First, distribute the negative sign to both terms in the second parenthesis:

$= 4x^6 + 8x^3 - 7x^2 - 6x^3$

Now, combine like terms. The like terms here are $8x^3$ and $-6x^3$:

$= 4x^6 + (8x^3 - 6x^3) - 7x^2$ $= 4x^6 + 2x^3 - 7x^2$

So, the expression simplifies to:

$4x^6 + 2x^3 - 7x^2$

Would you like further details or have any questions?

Here are 5 related questions to consider:

1. How do you identify like terms in a polynomial expression?
2. What happens when you distribute a negative sign across a binomial?
3. How can you verify your solution by substituting a value for $x$?
4. What are the steps for factoring a polynomial?
5. How can this expression be used in solving equations?

Tip: Always simplify terms with the same degree (like terms) in order to make polynomial expressions more manageable!