You want to derive I -> ~D from the premises (F & G) v(H &~I) and I -> (F & D) ? By the way, these are premises not assumptions - you shouldn't write "assume" after them as you are not introducing an assumption scope. Anyway, I -> F & D implies I -> D, and if you also have I -> ~D then we must have that I is false. (Because if I -> D and I -> ~D, then either D or ~D is false, so I implies a falsehood, which must mean I is itself false).
But I need not be false, because the assignment I, F, G, H, D = true satisfies the premises. Therefore we cannot derive I -> ~D from the premises.
To say that again: if we take the premises together with I -> ~D, we reach the conclusion ~I. But from the premises alone, we cannot reach the conclusion ~I. Therefore, the premises cannot imply I -> ~D.
You have edited your answer to include the correct premises, (F & G) v(H &~I) and I -> ~(F & D) .
Suppose I. Then we obtain ~(F&D). Assume for contradiction F is false. This means F&G is false, so H&~I must be true, which cannot be under the assumption of I. Therefore F is true, which together with ~(F&D) means that D is false. So, this gives us I -> ~D by conditional proof.