(1+2):3+(4·5)-(6+7+8)

Let's solve the expression step by step.

The given expression is:

\[ (1+2):3+(4\cdot5)-(6+7+8) \]

1. First, calculate the values inside the parentheses:

   • \(1 + 2 = 3\)
   • \(6 + 7 + 8 = 21\)

2. Now, substitute these values back into the expression: \[ 3:3 + (4\cdot5) - 21 \]

3. Next, calculate \(4 \cdot 5\):

   • \(4 \cdot 5 = 20\)

4. Substitute this value into the expression: \[ 3:3 + 20 - 21 \]

5. Now, perform the division:

   • \(3:3 = 1\)

6. Substitute this value into the expression: \[ 1 + 20 - 21 \]

7. Now, perform the addition and subtraction:

   • \(1 + 20 = 21\)
   • \(21 - 21 = 0\)

Thus, the final result of the expression is:

\[ \boxed{0} \]