To solve the expression $42 \div 5 \times 4 \div 6$, follow the order of operations (PEMDAS/BODMAS), which prioritizes division and multiplication from left to right.

Step-by-Step Calculation:

1. First, perform the division: $42 \div 5 = 8.4$

2. Next, multiply the result by 4: $8.4 \times 4 = 33.6$

3. Finally, divide by 6: $33.6 \div 6 = 5.6$

So, the result of $42 \div 5 \times 4 \div 6$ is 5.6.

Would you like more details on how this works, or do you have any further questions? Here are some related questions to explore:

1. How would the result change if parentheses were added, such as $(42 \div 5) \times (4 \div 6)$?
2. What happens if we replace the division by 5 with multiplication by 5 in the same expression?
3. How do the results differ when using integer division (i.e., rounding to whole numbers)?
4. How do you evaluate more complex expressions with multiple operations?
5. What is the impact of changing the order of multiplication and division in multi-step problems?

Tip: Remember that division and multiplication are of equal priority, so always work from left to right when solving expressions with both!