Hey so say I've got a level 5 wizard, let's call him Larry.
Larry is wearing a +1 silken ceremonial armor and has a dexterity bonus of +2 giving him an AC of 14
+1 armor +1 enhancement +2 dex
Now Larry casts mage armor and shield
would the end result be
+4 armor +4 shield and +2 dex for an AC of 20
or
+4 armor +1 enhancement +4 shield +2 dex for an AC of 21
Another day he gets his level 5 druid friend to cast barkskin on him
would this result in
+1 armor +1 armor enhancement +2 natural armor enhancement +2 dex for an AC 16
or
+1 armor +2 enhancment +2 dex for AC 15
+4 armor, +4 shield, +2 dex, AC 20.
+1 armor, +1 enhancement, +2 natural, +2 dex, AC 16.
Enhancement Bonuses: Enhancement bonuses apply to your armor to increase the armor bonus it provides.
The enhancement bonus is only increasing the armor bonus of the Silken Ceremonial Armor, making it +2 instead of +1. The Mage Armor overlaps with the Silken Ceremonial Armor, so you take the better, which is the +4.
So, in the first scenario it is +4 armor +4 shield +2 Dex total AC 20.
Similarly, the enhancement bonus to natural armor from Barkskin adds to your existing natural armor bonus (even if that's +0), and natural armor bonus stacks with regular armor bonus.
So in the second case, it would be +2 armor (including the +1 enhancement bonus) +2 natural armor (including the +2 enhancement bonus) and +2 Dex for a total of AC 16.
Generally speaking, armor bonuses stack as long as they are different types and coming from different sources.
Mage Armor and the +1 silken ceremonial armor are both Armor bonuses, and so do not stack.
By default Larry has a +2 Armor bonus and a +2 Dexterity bonus, giving him an AC of 14. The Shield spell grants a +4 Shield bonus which stacks with Armor and Dexterity, and so brings his AC up to 18.
Casting Mage Armor normally gives a +4 Armor bonus. However Larry already has a +2 Armor bonus from his Silken ceremonial suit, and so the bonuses overlap instead of stack. If we continue the previous example, his AC would now be 10 (default) +4 (Armor) +4 (Shield) +2 (Dexterity) for a total of 20.
Barkskin is a little trickier. Barkskin is an Enhancement bonus to Larry's existing Natural Armor bonus. If Larry is a human, his natural armor bonus is +0. If Larry was a Kobold, his natural armor bonus would be +1. In both cases, Barkskin would stack with the natural armor bonus present. While not relevant to this particular example, this can be relevant in some other cases so I'd rather not completely gloss over it.
On the day Larry meets the druid, Larry's Armor Class would be 10 (default) +2 (armor) +2 (dexterity) +2 (enhancement bonus to Larry's Natural Armor bonus of +0) = 16
Thanks all
Also side question I think i remember seeing a low level spell (3rd or below) that granted a deflection bonus to AC
One that wasn't protection from alignment
does anyone know of what it is?
Shield of Faith
Bullet Shield is level 2 and gives a +4 to +8 deflection bonus, but only for firearms and other ranged attacks.
Shield of Faith is 1st level and gives +2 to +5.
Ward the Faithful is 3rd level, only affects those who worship the same deity as you, and gives +2 to +4 deflection to AC and resistance to saving throws.
Nereid's Grace is 1st level and gives your Cha modifier as a deflection bonus to AC if you have no visible armor.