Compare the ratios first
The ratio 4:3 is about 1.3333, while 3:2 is 1.5. A 4000 × 3000 image therefore has more height relative to its width than a 6 × 4 inch frame. Changing the resolution metadata does not change either ratio.
This situation often becomes visible when moving between 6 × 8 and 4 × 6 inch prints. The first has the 4:3 landscape shape; the second has the 3:2 shape. They are different compositions unless you allow borders.
Fill removes height
Keep the full 4000-pixel width and divide it by 1.5 to find the ideal crop height: 2666⅔ pixels. Compared with the original 3000-pixel height, 333⅓ pixels are removed. Because the width is unchanged, the removed area is one-ninth of the original, or about 11.11%.
At 6 × 4 inches, that retained rectangle gives about 666.67 PPI. A centred crop splits the removed height between the top and bottom. Moving it toward the upper part of the source protects the top and discards more from below. It does not change the ideal crop dimensions.
Understand fractional boundaries
A ratio can produce a mathematically exact crop boundary between pixels. The preview geometry can retain that precision, but a downloaded raster must have whole-pixel dimensions. Treat a displayed decimal as geometry, not a promise that a file can contain a fractional row of pixels.
PrintLilt reports the export’s resulting pixel dimensions. Small edge rounding should not be confused with stretching the whole photograph. If exact dimensions are critical downstream, inspect the downloaded file and use its actual pixel counts in the next calculation.
Fit adds side space
To keep every pixel, fit the source to the frame’s four-inch height. A 4:3 image at that height is 5⅓ inches wide. The six-inch frame has two-thirds inch left over, giving one-third inch on each side when the image is centred.
All 4000 × 3000 pixels remain, and the image has 750 PPI. The higher PPI does not make fit automatically preferable: the picture is physically narrower within the same frame. The visible borders and the retained composition are the relevant tradeoff.
Choose with the subject in view
Check whether the crop removes heads, feet, foreground detail, or a line of text. If it does, move the crop before rejecting fill entirely. If no position retains what matters, use fit or select a 4:3 print size.
Export the cropped photo when another application will place it, or include the complete frame when the borders are part of the intended image. A paper-layout PDF preserves physical placement, but the printer must still use actual-size settings. Keep the source so the alternate composition remains available.