Complex sentence: Throughout May and June the 2/4th played an important role in the landing unopposed on Sadau Island and then, a few days later on 3 May at Tarakan where it once again acted in support of the 26th Brigade.
Split into simpler sentences: Throughout May and June the 2/4th played an important role in the campaign. The landing on Sadau Island was unopposed, however, and a few days later on 3 May at Tarakan it was once again tasked to act in support of the 26th Brigade.