The dress cost 4×96=$384 and so the cost of dress and shoes is $480 so the purse cost 780-480=$300.
But the question can be interpreted differently. If the dress cost 4 times the cost of the shoes and the purse together then the dress cost 4(96+purse)=384+4×purse. Add on the cost of the shoes and the purse:
480+5×purse=780. So 5×purse=300 and the purse cost $60.
This means that the dress cost $156×4=$624. Cost of the three items: 624+96+60=$780.