To solve the given expression, we need to perform the arithmetic operations step-by-step. Let's break it down:

### Numerator Calculation:
\[ 2.5 \times 4.3 - 1.7 \times 7.8 + 3.5 \times 2.5 \]

1. Calculate \( 2.5 \times 4.3 \):
\[ 2.5 \times 4.3 = 10.75 \]

2. Calculate \( 1.7 \times 7.8 \):
\[ 1.7 \times 7.8 = 13.26 \]

3. Calculate \( 3.5 \times 2.5 \):
\[ 3.5 \times 2.5 = 8.75 \]

Now, combine these results:
\[ 10.75 - 13.26 + 8.75 \]

First, subtract \( 13.26 \) from \( 10.75 \):
\[ 10.75 - 13.26 = -2.51 \]

Then, add \( 8.75 \):
\[ -2.51 + 8.75 = 6.24 \]

So, the numerator is:
\[ 6.24 \]

### Denominator Calculation:
\[ 10.4 + 11.5 + 12.6 - 11.8 - 10.7 - 9.6 \]

1. Add the positive terms:
\[ 10.4 + 11.5 + 12.6 = 34.5 \]

2. Add the negative terms:
\[ 11.8 + 10.7 + 9.6 = 32.1 \]

Now, subtract the sum of the negative terms from the sum of the positive terms:
\[ 34.5 - 32.1 = 2.4 \]

So, the denominator is:
\[ 2.4 \]

### Final Calculation:
\[ P = \frac{6.24}{2.4} \]

Divide \( 6.24 \) by \( 2.4 \):
\[ \frac{6.24}{2.4} = 2.6 \]

Therefore, the value of \( P \) is:
\[ P = 2.6 \]