What is the difference between the largest and smallest numbers that you can make with the digits 6, 3, 9 and 8 without repetition?
[3 marks]

To find the greatest 4-digit number with the given digits, we arrange the digits in descending order.
[0.5 marks]

And, to find the smallest 4-digit number with the given digits, we arrange the digits in ascending order.

$\begin{array}{cccc}\text{Thousands}& \text{Hundreds}& \text{Tens}& \text{Ones}\\ 3& 6& 8& 9\\ 9& 8& 6& 3\end{array}$

[1 mark]

Since $3<6<8<9$ or $9>8>6>3,$ the smallest and largest numbers with the given digits are 3689 and 9863 respectively.
[1 mark]

The difference between these two numbers is 9863 - 3869 = 6174.
[0.5 marks]