Without the support from C, they would bounce (nothing move).

With the support from C, the move from B to A succeeds and the unit in A is dislodged.

These are very basic scenarios covered in the rulebook, which I would that you thoroughly read.

In the first example they bounce. If support is not somehow cut from C, then B will take territory A.

Here is a link to the rulebook

http://www.wizards.com/avalonhill/rules/diplomacy.pdf

Others are telling me that B and A would merely switch places, which is why I ask to verify the answer. It sounds like A -> B fails because the game considers that B is still in its territory even though it is moving. So what if another unit support moves A to B? B does not have a support hold and it is not holding, so do they swap places or bounce?

Two untis cannot swap places. The closest you can do to a swap is to move around in a circle with 3 territories.

Did the people telling you A and B will switch places also ask for your Chase Bank Account info yet?

If both have support to the same territory they again bounce.

Rulebook is clear - the only way for two units to swap places is to have one army move via land and the other army move via convoy. RTFM

Only way A and B can swap places is if there is an adjacent fleet that convoys one of the units. Let's say Italy has a Fleet in Gulf of Lyons and an Army in Marseilles and France has an Army in Spain. If France does A Spa -> Mar and Italy does A Mar -> Spa by convoy and F GoL convoys A Mar -> Spa then Spa and Mar will swap places.

Its possible that was the intention; to kidnap an army. I think this is technically allowed but webDip doesn't support it.

Thank you, abg. Yale, not yet :) Follow-on: Does a support move help in a retreat against an occupied territory?

Seriously, read the rules, this is a hard game to play if you don't understand basics of movement, support, dislodging, and retreating. The DATC also has lots of useful examples.

You cannot support a retreat

Supports have nothing to do with retreats. You can only retreat to a territory that was not attacked by any units. With the exception that a dislodged unit is not considered to have attacked the territory dislodging it. So let's say Germany does Mun->Bur and Ruhr supports Mun->Bur and France does Bur->Mun. Bur is dislodged by the attacking unit from Mun. Bur can not retreat to Mun, but any other unit adjacent to Mun could retreat to Mun if dislodged (for example if an Army in Kiel were dislodged on this same turn it could retreat to Mun since Mun is not considered to have been attacked by Bur).

I once dreamed of doing this, then trying to end up in a game with one of my advisors... asking them for advice... and clinically inserting the knife just when they thought I was a loyal stool pigeon!