It's about four sisters growing up. 老师。这里的growing up应该起名词作用吧?那怎么不是four sisters' 呢?
动名词作宾语时,其逻辑主语用主格或者宾格都可以,所以这里用four sisters 或者 four sisters' 都可以。
这里的about是介词,后面的动名词是它的宾语。又如:
I am sure of my brother / brother's passing the examination. 我确信我弟弟会通过考试。