#### Answer

(answers vary)
An example of a four-digit number that is divisible by $4$ but not by $8$ is $1244$.

#### Work Step by Step

(Note that there are a number of possible answers to this item.
RECALL:
(1) A number is divisible by $4$ if the last two digits form a number that is divisible by $4$.
(2) A number is divisible by $8$ if the last three digits form a number that is divisible by $8$.
The divisibility rules above suggest that the a four digit number will be divisible by $4$ but not by $8$ if
(a) the last two digits form a number that is divisible by $4$, but
(b) the last three digits form a number that is not divisible by $8$.
Notice that the four-digit number $1244$ has:
(a) its last two digits form the number $44$ which is divisible by $4$ since $44\div 4 =11$; and
(b) its last three digits form the number $244$ which is not divisible by $8$ since $244 \div 8 = 30.5$.
Thus, an example of a four-digit number that is divisible by $4$ but not by $8$ is $1244$.