Final answer:
Without specific context or reference, the activity Anne Frank wanted to do with her cousin Buddy Elias cannot be definitively identified, though she enjoyed reading, writing, and discussions.
Step-by-step explanation:
The question pertains to Anne Frank, a historical figure known for her diary which she wrote during the Holocaust while hiding from the Nazi regime. Anne had many normal wishes and desires, like any young teenager, despite the extraordinary circumstances she lived in. Her cousin, Buddy Elias, was one of the people she expressed her desires to.
However, without the specific context or a reference to the text from Anne Frank's diary or related literature, it's challenging to pinpoint the exact activity Anne wanted to do with Buddy Elias. Activities she enjoyed included reading, writing, and discussing her thoughts with others, which might be reflected in her communications with her cousin. Nevertheless, to provide an accurate and concrete answer, one would need to refer to direct citations from her diary or biographical information detailing her relationship with Buddy Elias.