Let's consider the possibilities for each stripe:

For the first stripe, we have three colour options - (red, green, yellow).

For the second stripe, we need to choose a colour different from the first stripe. So, we have two colour options.

For the third stripe, we need to choose a colour different from the second stripe. So, we have two colour options.

For the fourth stripe, we need to choose a colour different from the third stripe. So, we have two colour options.

So, total number of possible ways to design the flag = $3 \times 2 \times 2 \times 2 = 24$

Hence, option (C) is correct.