Complex sentence: During Operation Phantom Fury, Hussein's family left, but he stayed behind, "able to photograph not only the results of the attacks on Fallujah, (but) also able to photograph members of the insurgency on occasion," according to Lyon.
Split into simpler sentences: During Operation Phantom Fury, Hussein's family left, but he stayed behind. He photographed "not only the results of the attacks on Fallujah, (but) also... members of the insurgency on occasion," according to Lyon.