A whole number $n$ which when divided by $4$ gives $3$ as remainder. What will be the remainder when $2n$ is divided by $4$?

Given that when a whole number $n$ is divided by $4$, the remainder is $3$. We can express $n$ as:
$$n=4k+3$$

where $k$ is a non-negative integer ($k=0,1,2,\dots$).

To find the remainder when $2n$ is divided by $4$, we multiply the entire expression by $2$:

$$2n=2(4k+3)$$

$$2n=8k+6$$

We can rewrite $6$ as a combination of a multiple of $4$ and a remaining fractional residue:

$$2n=8k+4+2$$

$$2n=4(2k+1)+2$$

Since the term $4(2k+1)$ is completely divisible by $4$, the remaining part is $2$.
Therefore, when $2n$ is divided by $4$, the remainder is $2$.