Amount of differntial oil rear
 

The auto parts store said it would take under 3 qts.

I put 3 quarts in and put my finger in the whole and still could not feel oil. The plate on the diff said 15 to 40 mm below the top.

Any idea, in quarts, how much it should take?

Jay

What truck is this in? Does the cover have 10 bolts on it?

Should take 2 1/2 - 3 ish quarts of fluid. Just pour it in till it starts to come back out. Let it drain till it's done and put your plug back in - you're done.

I know this goes without saying... but I have to say it just incase. Your truck shouldn't be jacked up during filling. Fill your diff with the truck on level ground.
And Like Jon said.. Fill it till it begins to come back out... allow it to stop dripping out. Put the plug back in and you could also insure your differential vent is clear.

The tag on the diff says there should be 15 to 40 mm of space, so filling it till it fills up is contrary to the tag and the Clymer ?

To check your fluid level... You would have to stick your finger in the filler hole to see if it is just below the fill hole.
So... Once FULL, and the fluid has stopped dripping, stick your finger in the hole to displace some more excess fluid.
If your diff vent is clear, a little extra fluid won't do any harm