771:9+(506-105•4)=

To solve the expression \( 771:9+(506-105 \cdot 4) \), we follow the order of operations (parentheses, exponents, multiplication and division from left to right, and addition and subtraction from left to right).

1. Calculate \( 105 \cdot 4 \): \[ 105 \cdot 4 = 420 \]

2. Substitute this back into the expression: \[ 506 - 420 \]

3. Calculate \( 506 - 420 \): \[ 506 - 420 = 86 \]

4. Now substitute back into the expression: \[ 771:9 + 86 \]

5. Perform the division \( 771:9 \): \[ 771 \div 9 = 85.6667 \quad (\text{approximately}) \]

6. Add \( 85.6667 \) and \( 86 \): \[ 85.6667 + 86 = 171.6667 \quad (\text{approximately}) \]

So, the final result is approximately \( 171.67 \).