I think the question reads $660 less 10% plus $90=total amount. I understand "$660 less 10%" to mean 10% of $660=$66. That makes 660-66=$594 (90% of $660) plus $90=$684.
The question could also be interpreted "less 10% and (less) $90, so we subtract $90 from $594 instead of adding, to get $504.
Another interpretation is to add $90 before deducting 10%: 660+90=750, less 10% of 750=750-75=$675. Yet another interpretation is to deduct $90 before deducting 10%: 660-90=570 less 10%=570-57=$513.
To get $558 you need a total deduction of $102, which is 66+36 (10% plus $36 in deductions).