They would have done the task if they ... their best soldier.

Analysis:

This is a conditional sentence. The first clause is in the past perfect tense ('would have done'), which indicates a hypothetical situation in the past. The second clause should therefore be in the past perfect tense as well, using 'had' + past participle.

Let's look at the options:

• didn't lose - This is simple past, not past perfect.
• hadn't lost - This is past perfect and fits the structure of a third conditional sentence (If + past perfect, would have + past participle).
• wouldn't lose - This is conditional perfect, which is not used in the 'if' clause of a third conditional.
• will not lose - This is future tense, which is incorrect for a past hypothetical situation.

Therefore, the correct option completes the third conditional sentence, expressing an unreal condition in the past and its unreal result.

Answer:

hadn't lost