Let's solve the expression step by step:

$3 \times 6 \div 6 \times 3$

Following the order of operations (PEMDAS/BODMAS: Parentheses, Exponents, Multiplication and Division, Addition and Subtraction), we handle multiplication and division from left to right:

1. $3 \times 6 = 18$
2. $18 \div 6 = 3$
3. $3 \times 3 = 9$

So, the value of the expression is:

$\boxed{9}$

Would you like more details or have any questions?

Here are 5 related questions to explore further:

1. What is the order of operations in more complex expressions?
2. How does multiplication and division work in longer chains of operations?
3. What happens when parentheses are added to an expression?
4. How do fractions affect multiplication and division problems?
5. How would the expression change if exponents were introduced?

Tip: Always work from left to right when dealing with multiplication and division in the same step of the order of operations.