PhD - which statistical analysis to use? MLM, t tests, ANOVA?

Hi, my research question is "do large cognitive changes precede a period of mood stability?" (N = 30), I have 20 therapy sessions data for each participant, which includes scores on a cognitive style questionnaire and scores on a mood questionnaire of each session.

My supervisor has suggested that I define mood stability by assessing an index of the mean squared point-to-point change in mood scores across clusters of four subsequent therapy sessions for each participant.

Now how do I go about analysing and answering the research question?

Any help would be much appreciated.