# Mattaniah ... Mika ... Zabdi ... Asaph ... Bakbukiah ... Abda ... Shammua ... Galal ... Jeduthun

These are the names of men.

# who began the thanksgiving in prayer

That is, who directed the singers.

# Bakbukiah, the second among his brothers

Bakbukiah was Mattaniah's kinsman and second in authority to Mattaniah or "Bakbukiah, who led a second group of singers."

# brothers

"associates" or "fellow workers"