The greatest number which divides $990$ and $1330$, leaves remainder $6$ and $10$ respectively is:

To find the required greatest number, we subtract the respective remainders from the numbers and then find the Highest Common Factor (HCF) of the resulting values.
$$990-6=984$$

$$1330-10=1320$$

Now, find the HCF of $984$ and $1320$:
Using prime factorization or division method:

$$1320=984\times 1+336$$

$$984=336\times 2+312$$

$$336=312\times 1+24$$

$$312=24\times 13+0$$

Since the final remainder is $0$, the HCF is $24$.
Therefore, the greatest number is $24$.