As per the question,

$AB \times CD = DEF$ …… (i) And, $DEF + GHI = 975$ …… (ii)

$E = 0$, and $F = 8$

So, equation (ii) can also be written as, $D08 + GHI = 975$

Let’s consider the given sum, i.e. $D08 + GHI = 975$

At unit’s place of the resulting sum we have 5. This is possible only if $I = 7$.

So, $8 + 7 = 15$. So, we will get a carry of 1.

Now, $1 + 0 + H = 7$ Or $H = 6$

Now, $D + G = 9$. This can be obtained in following ways: $9 + 0$, $8 + 1$, $7 + 2$, $6 + 3$, $5 + 4$

Since, value of E is 0, therefore $9 + 0$ can be eliminated. Since value of F is 8, therefore $8 + 1$ can be eliminated. Since value of I is 7, therefore $7 + 2$ can be eliminated. Since value of H is 6, therefore $6 + 3$ can be eliminated.

Therefore, the values of D and G must be 4 or 5.

Let’s consider the given sum, i.e. $D08 + GHI = 975$, again. If $D = 4$ and $G = 5$, $408 + 567 = 975$ If $D = 5$ and $G = 4$, $508 + 467 = 975$

Now, considering equation (i). If $D = 5$, $AB \times C5 = 508$. This is not possible, as on multiplying any number that has 5 as unit’s digit, with any other number, we get either 0 or 5 as the unit’s digit in the resultant number.

If $D = 4$, $AB \times C4 = 408$. This is possible. So, $D = 4$, and $G = 5$.

Let’s list down the digits: $A = ?$ $B = ?$ $C = ?$ $D = 4$ $E = 0$ $F = 8$ $G = 5$ $H = 6$ $I = 7$

Now, we are only left with the digits 1, 2, 3, and 9

Analyzing $AB \times C4 = 408$, we can see that $12 \times 34 = 408$

Therefore, $A + B + C = 1 + 2 + 3 = 6$

Hence, option (A) is correct.