Solution -

The question asks us how many socks have to be chosen at random in order for us to be SURE that we chosen at least two socks of the same colour.

The information given in the question is -
Black socks = 8 as there are 4 pairs of black socks,
Gray socks = 6 as there are 3 pairs of gray socks,
Orange socks = 4 as there are 2 pairs of orange socks.

Out of them, if 3 socks are removed,
then it can be 2 socks of one colour and 1 sock of another colour,
OR
3 socks of one single colour,
OR
1 of each colour, each of the 3 socks is of 3 different colours.

Since 1 of each colour is possible, and hence, we might not get a pair.

If 4 socks are removed, then it can be 1 of each colour and the 4th sock removed has to form a pair with one of the three colours.
If we consider any other case, it will also have a pair.

Hence 4 should be the minimum.

Therefore, the correct answer is option A.