Let's break down the expression step by step:

$3 \cdot 6 - \frac{6}{3}$

1. Multiply first: $3 \cdot 6 = 18$.

2. Divide next: $\frac{6}{3} = 2$.

3. Subtract: $18 - 2 = 16$.

So, the final result is $16$.

Would you like more details or further clarification?

Here are 5 related questions to explore:

1. What happens if you change the multiplication in this problem to division?
2. How would the expression change if you added parentheses around $6 - 6$?
3. Can you solve a similar expression with fractions, like $\frac{9}{2} \cdot 4 - \frac{8}{4}$?
4. How does the order of operations (PEMDAS) affect this type of expression?
5. How would the result change if the division was done first?

Tip: Always remember to follow the order of operations (PEMDAS) — Parentheses, Exponents, Multiplication/Division (left to right), Addition/Subtraction (left to right).