OY. Manuals are for those who need to ask. If you would rather know what it all means then see Car Bibles : The Engine Oil Bible : Viscosity .

0W-40 is a good spec for "anytime anywhere". However I live in Florida and my crossie is garaged so I read the spec as needing at least 40 weight oil. The MB spec is more for the additive mix and the time before it breaks down (the "change oil" light.

Synthetic is good but is often thinner than conventional oils because they do not break down over time and use. The original Mobil 1 was about a 15 weight oil. No "w" because it did not change much. Also the most common oil at the time was a 10W-30 which started out in the middle and had long chain polymers added to imrove the specs. As time went by the long chains became shorter chains and the 10w-30 befame someting more like a 15-20 weight.

When I ran dino, after about 2-3k miles I'd see about a 2 psi drop in the idle oil pressure (resulting from the degredation) and change the oil and filter.

Synthetics are much better about winter flow and maintaining viscosity so an 8k oil change is reasonable. OTOH the 40 part indicates the minimum viscosity MB considers enough to support the engine (mainly the rod bearings) at high rpm (force increases with the square of the RPM) .

So for me, no 0w-30, 5w-30, 15w, or 20W-20. Nothing unless the top number is 40, (10w-40 would be ok or even straight 40 racing oil since it is unlikely to ever be started with an oil temperature under 50F.
20W-50 would be a maybe but only in extremis (I'd rather add a quart of ATF).

But for me and here and with a well broken in engine, synthetic 0W-40, 5W-40, 10W-40, 15W-40, or 20W-40 macht nichts.