21:3·6-(18+14) :8

Let's solve the expression step by step:

1. Start with the expression: \[ 21:3 \cdot 6 - (18 + 14) : 8 \]

2. Perform the division \( 21:3 \): \[ 21 \div 3 = 7 \]

3. Multiply the result by 6: \[ 7 \cdot 6 = 42 \]

4. Now, calculate the sum inside the parentheses: \[ 18 + 14 = 32 \]

5. Then, perform the division \( 32 : 8 \): \[ 32 \div 8 = 4 \]

6. Now substitute the results back into the expression: \[ 42 - 4 \]

7. Finally, subtract the results: \[ 42 - 4 = 38 \]

Thus, the final answer is: \[ \boxed{38} \]