Let's subtract the given expressions step by step:

You are asked to subtract:

$(6a^4b^4 + 2a^3b^6 - 4) - (a^4b^4 + 6a^3b^6 - 5)$

First, distribute the negative sign to the second expression:

$= 6a^4b^4 + 2a^3b^6 - 4 - a^4b^4 - 6a^3b^6 + 5$

Now, combine like terms:

1. Combine the $a^4b^4$ terms: $6a^4b^4 - a^4b^4 = 5a^4b^4$

2. Combine the $a^3b^6$ terms: $2a^3b^6 - 6a^3b^6 = -4a^3b^6$

3. Combine the constant terms: $-4 + 5 = 1$

So, the result of the subtraction is:

$5a^4b^4 - 4a^3b^6 + 1$

This is the simplified expression after performing the subtraction.

Do you need more details or have any questions?

Here are 5 related questions to consider:

1. How do you factor terms like $a^4b^4$ or $a^3b^6$?
2. How do you simplify polynomials with more complex terms?
3. Can you subtract polynomials with more variables, such as three or four variables?
4. How does the distributive property work when subtracting polynomials?
5. What is the significance of like terms in polynomial operations?

Tip: Always carefully distribute the negative sign across all terms when subtracting polynomials to avoid sign errors!