To simplify the expression \((6x^3 - 7x^2) - (7x^3 + 8x^2 - 7x^4)\), we first distribute the negative sign across the second polynomial:
\[ (6x^3 - 7x^2) - (7x^3 + 8x^2 - 7x^4) = 6x^3 - 7x^2 - 7x^3 - 8x^2 + 7x^4 \]
Next, we can combine like terms. Let's reorder the expression:
\[ 7x^4 + (6x^3 - 7x^3) + (-7x^2 - 8x^2) \]
Now, simplify the coefficients for each term:
- For \(x^4\): \(7x^4\)
- For \(x^3\): \(6x^3 - 7x^3 = -1x^3 = -x^3\)
- For \(x^2\): \(-7x^2 - 8x^2 = -15x^2\)
Putting it all together, we have:
\[ 7x^4 - x^3 - 15x^2 \]
Thus, the simplified expression is:
\[ \boxed{7x^4 - x^3 - 15x^2} \]