# This matter became sin to the family of Jeroboam

"Jeroboam's family sinned by doing this thing" 

# This matter

This phrase refers to Jeroboam's setting up shrines and appointing priests.

# caused his family to be destroyed and to be exterminated

"because of this God destroyed and exterminated Jeroboam's family" 

# to be destroyed and to be exterminated

"to be completely destroyed"