To find the value of the expression [tex]\(3 \times[64 \div(13-5)-4] \times 42 \div 6\)[/tex], we will evaluate it step-by-step following the order of operations: parentheses first, then division and multiplication from left to right.
1. Evaluate the expression inside the parentheses:
[tex]\[
13 - 5 = 8
\][/tex]
2. Division within the brackets:
[tex]\[
64 \div 8 = 8.0
\][/tex]
3. Subtract 4 from the result of the division:
[tex]\[
8.0 - 4 = 4.0
\][/tex]
4. Multiply the result by 3:
[tex]\[
3 \times 4.0 = 12.0
\][/tex]
5. Multiply the result by 42:
[tex]\[
12.0 \times 42 = 504.0
\][/tex]
6. Finally, divide the result by 6:
[tex]\[
504.0 \div 6 = 84.0
\][/tex]
Thus, the final result is:
[tex]\[
\boxed{84.0}
\][/tex]
