The sentence is an example of reported (indirect) speech in the past tense: "Musa asked Asmau what she _____ since he last saw her."

The reporting verb "asked" is in the past tense. The action being referred to occurred before the time of asking.The word "since" indicates an action that began in the past and continued up to a point. To express a continuous action in the past before another past event, we use the past perfect continuous tense: "had been doing"