Twelve is where the rows-and-columns question actually matters, because the two arrangements go to different places.
3 by 4 is three rows and four columns. Wide. A 4000 × 3000 photo gives twelve 1000 × 1000 px tiles, and the whole thing is wider than it is tall. That is the arrangement for a wall of twelve prints in landscape orientation, or a twelve-sheet poster.
4 by 3 is four rows and three columns. Tall. That is the Instagram one. A profile grid is three columns wide, so a picture spread across four rows needs four rows of three tiles, not three rows of four. Get this backwards and you will upload twelve tiles that assemble into something unrecognisable. The arrangement toggle on this page is labelled with rows first for exactly that reason.
Twelve tiles is a lot of manual uploading, so it pays to check the preview before exporting rather than after. Drag the interior lines if a subject sits on a seam. With three interior vertical lines and two horizontal ones in a 3 by 4, there are five chances for a cut to land somewhere awkward.
The split runs on a canvas in this page. Twelve tiles from a 40 megapixel source is still fast, because each tile is drawn and encoded on its own rather than the whole image being held on one canvas.