It looks like a flight to or from New Zealand which appears to be the only destination with a limit of both 23kg and one piece of luggage to/from HKG.

HK$1300/NZD$200 per extra piece and an extra HK$1300 if oversized (158cm limit vs. the regular allowance size limit of 203cm) And though it should not apply in this case, another HK$1300 if overweight so HK$2600 for overweight and oversized.

Looks like the flugelhorn or whatever it is should be checked as the first piece since that one can be up to 203cm total and 23kg. Second piece which one assumes is smaller than the 180cm of the ottoman or whatever, would just be the extra luggage piece charge of HK$1300/NZD$200 and not HK$2600.

This is like one of those logic puzzles. The combined weight is X and under the 23kg limit, the size of a mystery thing Y is under 180cm but must weigh less than 23kg, and the other thing Z, its weight added to the weight of thing Y is less than 23kg but you are not told the size of Z.

OP suggestion: Just say how big each thing is and what it weighs. But the CX website is clear enough, step by step with sizes and weights. The biggest catch is that the 2nd piece is not allowed to be as big as the first piece. So the 180cm is the first piece and the more compliant one is the 2nd piece.