The question asks for the correct expanded ratio when the initial ratio of $A : B : C = 2 : 3 : 4$.

To expand the ratio, let's first understand that we need to find a form where each part of the ratio is scaled similarly. Let's examine each option:

1. Option 1: $8 : 9 : 16$
   If we multiply the original ratio $2 : 3 : 4$ by 4, we get: $2 \times 4 : 3 \times 4 : 4 \times 4 = 8 : 12 : 16$ So, this option does not match because it has $9$ as the middle term.

2. Option 2: $8 : 9 : 12$
   Similar to above, scaling $2 : 3 : 4$ by any factor will not yield $8 : 9 : 12$, as the middle term remains 9, which is inconsistent.

3. Option 3: $8 : 9 : 24$
   Once again, scaling cannot give us $9$ as a term in the middle, so this is also incorrect.

4. Option 4: $4 : 9 : 16$
   To see if this could be correct, we can try checking if each number in this ratio maintains the relation $2 : 3 : 4$. Dividing each term by their common factors: $4 : 9 : 16 \neq 2 : 3 : 4$