If 300 dpi is your target print density, *in theory* the FC200 camera should be able to produce sharp prints up to around 15" x 11":
(4288 pixels /300 dpi = 14.6") x (3288 pixels / 300 dpi = 11")
But in real life, this camera has lots of limitations. It's fine for web photos and videos, but large prints - I think not so much. This is still a small-sensor camera, with components originally designed for use in security cam / web cam type applications. This camera has poor low-light performance (noisy) so bright sunlit scenes will work best. Some units have sharpness issues, likely a lens-mounting QA problem where one side or corner is noticeably less sharp.
"Good enough" for large prints of course is subjective, and depends on both subject matter and your personal taste.
The one thing it has going for it is the ability to shoot in Adobe DNG RAW format. This allows you to bypass the excessive in-camera sharpening and over-compression that it applies to JPEGs. With practice, you can get much better results by processing the RAW files yourself in apps like Lightroom or Photoshop.
Disclaimer: I haven't made any prints with this camera, but I do lots of large prints with Canon DSLR images. My suggestion is to give it a try. Places like Costco do high-quality 16x20 prints for around six bucks.