"I do not think she prepared this phase."
Translation:Je ne pense pas qu'elle ait préparé cette étape.
This is in the past subjunctive (instead of the past indicative) as it has been triggered by penser que in the negative.
Had it been a positive statement -
"I think she has prepared this phase" →
Je pense qu'elle a préparé cette étape
- the indicative would have been fine but, as it is negative, the subjunctive is required:
"I do not think she prepared this phase" →
Je ne pense pas qu'elle ait préparé cette étape.
When you are unsure which to use, this tool is invaluable:
Wow, that is some round about thinking by Duo. A synonym of phase is stage and another word for a (theatrical) stage in French is plateau which is, indeed, masculine. See these:
Ghost in the machine?