Four people ($1,2,3,4$) each pick a different fruit – apple, banana, cherry and date. The person who picked the apple is next to the person who picked the banana and not next to the person who picked the date. The person who picked the cherry is next to the person who picked the date. The correct combination is :

Let's evaluate the conditions given in the puzzle step by step for the sequence of positions $1,2,3,4$:
Conditions:

1. Apple is adjacent to Banana.
2. Apple is NOT adjacent to Date.
3. Cherry is adjacent to Date.

Let's check Option C:

* Position $1$: Apple
* Position $2$: Banana
* Position $3$: Date
* Position $4$: Cherry
* Condition 1 Check: Apple ($1$) is next to Banana ($2$). $⟹$ True
* Condition 2 Check: Apple ($1$) is next to Banana, which is not Date ($3$). $⟹$ True
* Condition 3 Check: Cherry ($4$) is next to Date ($3$). $⟹$ True

Since option C satisfies all constraints perfectly, it is the correct combination.