What is the AC of a figment creature, such as that created by Silent Image? For context, in Pathfinder it is 10 + size modifier.
Images created by silent image have no AC RAW
The result of silent image is not a creature or an object; it is an image.
You create the image of an object, a creature, or some other visible phenomenon that is no larger than a 15-foot cube. The image appears at a spot within range and lasts for the duration. The image is purely visual; it isn't accompanied by sound, smell, or other sensory effects.
Nowhere in the spell does it describe any rules for assigning the image an AC.
Compare this with mirror image which says:
A duplicate's AC equals 10 + your Dexterity modifier.
This is a special case because the illusion in mirror image is moving with the caster and thus makes sense to have an AC based on the caster's stats. However, this doesn't make much sense, for example, for an illusory stationary potted plant to use that same rule. So this is not going to work as a general rule for assigning an AC to illusions. However it does show us that if a spell intended to assign an AC to an illusion it would say so in the spell.
Since silent image doesn't describe any kind of AC and there is no general rule for assigning AC to illusions, then we must conclude that the things created silent image simply have no AC.
It also makes sense since AC is:
how well your character avoids being wounded in battle. Things that contribute to your AC include the armor you wear, the shield you carry, and your Dexterity modifier.
And an image obviously has no effective armor, can't dodge attacks, and has no dexterity. So it makes sense to have the enemy hit it without needing to roll against an AC.
The same holds true with minor illusion and major image as well.
So how does this work practically?
If an enemy tries to attack a silent image, most likely the DM will simply say that they interact with the image and thus know it is an illusion with no roll needed. This would seem to be the option that the rules would suggest.
Even though deducing an illusion using intelligence requires a check this still makes sense. Physically interacting with an illusion is by far the easiest and most straight forward way to check if something is an illusion. A good illusion is very difficult to discern by sight, but very few will stand up to any sort of physical interaction at all. Also, the spell says nothing about having to make any sort of check to interact physically; if the DM allows it, it simply happens.
DMs can assign the images AC in cases where it makes sense
Obviously, illusions have a huge variety of uses and use cases. Even though the rules imply the general rule is that images have no AC, the DM may encounter cases in which it does not make sense for an attack to automatically succeed.
In cases like these if the DM wants to simulate a miss chance or some other possibility that would make AC useful they may just have to assign the creature an AC and have the monster roll an attack against that. Then, if they hit, reveal that it is an illusion due to physical interaction. However, they will have no guidance from the rules about what AC to assign. They'll have to adjudicate it on a case by case basis.
This depends on the situation, as usual.
For, say, a character at his leisure, facing an unmoving image such as a Minor Illusion cantrip produces, the player might say "I'll poke it with my sword", and I'll respond "Your sword goes through it, and you realize it's an illusion; no roll needed. Conversely, if it's a combat situation, and the caster is actively moving the image, then it shouldn't be an automatic hit. The spell allows for an observer to use his action to make an Investigate roll, so that's not automatic, either. Why would that even be an option if you could automatically succeed with a physical interaction?
The closest answer I can see is that when you cast a Mirror Image spell, an attacker first determines whether he is swinging at an image or at the real thing. If an image, it is called out as having an AC of 10 + the caster's Dex. Unless something different is called out, I would probably use that as an available option. The observer can use his action to try to Investigate (vs. Spell DC) as the Silent Image spell mentions, or I would allow him to use his action to try to physically interact (vs. AC) to determine its nature, if he thinks that's a more likely strategy for him.