What they're specifying is the number of pixels per axis, not really any actual size requirements. Multiply 24 by 180, you get 4,320 pixels on the long dimension. Multiply 16 by 180 and you get 2,880 pixels on the short dimension. Your camera is 12 MP, basically.
Do the same math with their specification, you get 3,000 by 1,800 pixels. They are specifying a 5:3 aspect ration instead of the 3:2 that most cameras shoot (based on the original 35mm frame size,) but you can see that the pixel count in your images exceeds their specification.
300dpi is a publishing standard of sorts, and if you tried to print your image at 24 inches and 300 dpi, it would get a dithered, pixelated look in the printing process. It still well exceeds their pixel density at the size they specified.
Another way to look at it is that 180 dpi is 6-tenths of 300 dpi. Take 6-tenthes of your dimensions and if that's larger than their 10 x 6, then you're good. 6-tenths of 24 is 14.1, well over 10. 6-tenths of 16 is 9.6, again well over their 6.
Your images have the required pixel density, unless you crop them severely. As for cropping, you can figure out the limit for that easily enough. Don't go less that 3,000 x 1,800. That's all there is to it. 3,000 x 1,800 pixels, you're good.