The Double Fishermans Knot is used for tying together two lines of the same diameter.
Imagine for example you need to anchor stern-to the beach and need to take a long line to an object ashore. Your mooring lines are not long enough for the job and need to be joined together. The Double Fishermans Knot would be the knot to use to make this connection.
The two double overhand stopper knots come up against each other when the standing parts are pulled apart making this knot - correctly speaking it's a bend, not a knot - much stronger and more secure than a reef knot.
Although it can be formed more quickly and easily with single overhand knots, it won't be anywhere near as strong as the version shown here.
Lay two lines together and take the right-hand (yellow) one over the left-hand (red) one;
Pass working end of the yellow line under its own standing part and the red line's working end working from left to right;
Do the same again forming two loops around the red line;
Now tuck the working end of the yellow line back through the two yellow loops, and tighten the knot (it's a double overhand knot) around the red line;
Transfer your attention to the red line and repeat the process to form two red loops.
Tuck the working end of the red line through the two red loops from left to right.
Cinch the red double overhand knot up tight.
Pull the two standing parts until the two knots are jammed together - and that's it, you've tied a double fishermans knot.