Which of the numbers given below is exactly divisible by 24?

A number is exactly divisible by $24$ if it is co-prime divisible by both $3$ and $8$ ($24=3\times 8$).
1. Divisibility rule for 8: The last three digits of the number must form a number divisible by $8$.
2. Divisibility rule for 3: The sum of all digits of the number must be a multiple of $3$.

Let's test each option:

* Option A: 14744
* Last $3$ digits: $744$. Since $744÷8=93$, it is divisible by $8$.
* Sum of digits: $1+4+7+4+4=20$. Since $20$ is not a multiple of $3$, $14744$ is not divisible by $3$.

* Option B: 28856
* Last $3$ digits: $856$. Since $856÷8=107$, it is divisible by $8$.
* Sum of digits: $2+8+8+5+6=29$. Since $29$ is not divisible by $3$, $28856$ is not divisible by $3$.

* Option C: 43976
* Last $3$ digits: $976$. Since $976÷8=122$, it is divisible by $8$.
* Sum of digits: $4+3+9+7+6=29$. Not a multiple of $3$, so it is not divisible by $3$.

* Option D: 57528
* Last $3$ digits: $528$. Since $528÷8=66$, it is divisible by $8$.
* Sum of digits: $5+7+5+2+8=27$. Since $27$ is a multiple of $3$ ($27÷3=9$), it is divisible by $3$.

Since $57528$ satisfies both divisibility rules, it is completely divisible by $24$.
Verification: $57528÷24=2397$.