This is the 15272nd most frequent Russian word.
посещениями
"Visits" (instrumental plural form).
In this sentence, "посещениями" refers to activities of visiting museums and theaters, highlighting the plural form of the noun in instrumental case to indicate means or measures.
Ее график был насыщен посещениями музеев и театров.
Her schedule was filled with visits to museums and theaters.
The word "посещениями" here is used to express "visits" in plural and instrumental case, emphasizing the value of participation in events.
Он гордился своими посещениями научных конференций.
He was proud of his visits to scientific conferences.
Here, "посещениями" captures the notion of the actual visits made, contextualized in plural and instrumental case, showing the subject's positive feelings about them.