Subtract the sum of `x^(2)-5xy +2y^(2) and y^(2)-2xy -3x^(2)` from the sum of `6x^(2)-8xy-y^(2)` and `2xy-2y^(2)-x^(2)`.

Answer

To solve the problem, we need to follow these steps:

### Step 1: Identify the expressions
We have two sets of expressions to work with:
1. The first set: \(6x^2 - 8xy - y^2\) and \(2xy - 2y^2 - x^2\)
2. The second set: \(x^2 - 5xy + 2y^2\) and \(y^2 - 2xy - 3x^2\)

### Step 2: Calculate the sum of the first set
We will first add the two expressions in the first set:
\[ (6x^2 - 8xy - y^2) + (2xy - 2y^2 - x^2) \]

Combine like terms:
- For \(x^2\): \(6x^2 - x^2 = 5x^2\)
- For \(xy\): \(-8xy + 2xy = -6xy\)
- For \(y^2\): \(-y^2 - 2y^2 = -3y^2\)

So, the sum of the first set is:
\[ 5x^2 - 6xy - 3y^2 \]

### Step 3: Calculate the sum of the second set
Now, we add the two expressions in the second set:
\[ (x^2 - 5xy + 2y^2) + (y^2 - 2xy - 3x^2) \]

Combine like terms:
- For \(x^2\): \(x^2 - 3x^2 = -2x^2\)
- For \(xy\): \(-5xy - 2xy = -7xy\)
- For \(y^2\): \(2y^2 + y^2 = 3y^2\)

So, the sum of the second set is:
\[ -2x^2 - 7xy + 3y^2 \]

### Step 4: Subtract the second sum from the first sum
Now we need to subtract the sum of the second set from the sum of the first set:
\[ (5x^2 - 6xy - 3y^2) - (-2x^2 - 7xy + 3y^2) \]

This simplifies to:
\[ 5x^2 - 6xy - 3y^2 + 2x^2 + 7xy - 3y^2 \]

### Step 5: Combine like terms again
Combine the like terms:
- For \(x^2\): \(5x^2 + 2x^2 = 7x^2\)
- For \(xy\): \(-6xy + 7xy = xy\)
- For \(y^2\): \(-3y^2 - 3y^2 = -6y^2\)

So, the final result is:
\[ 7x^2 + xy - 6y^2 \]

### Final Answer:
\[ 7x^2 + xy - 6y^2 \]