Can this bag be considered a carry on? Dimensions are 12" x 22" x 12"!?

Since most airlines know that not everyone has luggage in exactly those dimensions, they also set a maximum total measurement of 46 inches.

According to the website, the dimensions are 12 x 24 x 12. If you add all of those together, you come up with 48.

That is only 2 more than the maximum. You are over one dimension by couple of inches, but less on the others. I do not think that anyone will notice. Really.

All gates have a metal frame into which the gate agent can ask you to fit your carry on, but I don't recall ever seeing a gate agent ask someone to test their carry on in that frame.

Just by the dimensions it is too big but as a duffel bag you can "decrease" the size by not packing it full. As long as it fits into the overhead bin you should have no problem. BTW Southwest allows 2 free checked bags, why don't you just check this.

If Southwest goes by the volume of the bag (which I don't think is the case) then your duffel bag is way too large. I would call southwest airlines and tell them the dimensions; see what they say.

Depends on the flight attendant.

It exceeds one of the maximum dimensions, AND exceeds the "total measurement" rule, but being a soft duffel I have little doubt it will fit in the overhead bin.

Get a grumpy gate attendant and you'll be forced to check it, but I bet nine time out of ten they don't even look twice at that bag.

no.

the bag you have is larger than allowed - that 6 inches in length may be pretty noticable.

If you can add an external luggage strap, and fold it down to 18" or less in length, then you might get away with it. The airline may require you to check this bag, so pack it carefully.

Your bag is too big, and unlike most airlines they are very specific about the dimensions. (Most talk about total linear dimension, not specific side lengths.) This is because SW overheads are pretty small.

Hmmm... math. Got it! 12 is bigger than 10!

So, buy the rules it does not qualify. I don't know, however, how picky they are about their measurements. I you don't pack it tightly, you can probably get it to squish into a 10×16×24 space.