Is this the right size for a 24x16 room?

Generally, a 9,000 BTU will be a bit too small as it is best suitable for rooms around 250 sqft. For a 24x16 room, ~400sqft, a 12,000 BTU unit will be an excellent choice as it can properly service a room up in the 500sqft range. Below is a link to our Mitsubishi 12,000 BTU wall mounted mini-splits. However, sizing has many determining factors such as geographical location, insulation quality, etc... so please keep those in mind as well. If you have any further questions or would like addition assistance please feel free to give us a call! Thank you. https://hvacdirect.com/ductless-mini-splits/single-zone-ductless-mini-splits/filter/12000-btu-1-ton-btu-tonnage/mitsubishi/wall-mounted.html