A 12MP image is about pixel dimensions, not file size. The 300 dpi setting is mainly print metadata and does not by itself make the file larger. The main reason your export is only 5–6MB is likely JPEG compression: JPEG file size depends on image content and compression quality, so a 12MP file can easily be smaller than 9MB.

Black-and-white can also compress more efficiently than a detailed color image, which may further reduce the file size. So a smaller MB size does not mean the image is not 12MP.

What matters is whether the exported image has roughly 12 million pixels and meets the contest’s format requirements. Check the pixel dimensions in Lightroom or your file properties. If the contest truly requires a minimum file size, you may need to export with higher JPEG quality or in a less-compressed format if allowed. But don’t assume that 9MB is the definition of 12MP—they are different measurements.