How does channel divinity work?

Clerics gain the ability to channel divine energy and depending on your Domain and level you can use your "channel divinity" for different abilities. The amount of times you can use a "channel divinity" ability is limited, depending on your level, as stated in the PHB (pp. 58f).

Can a 4th level cleric give a character 20 HP?

Yes, a cleric with the Life Domain can restore 5× his cleric level hit points using channel divinity for his Preserve Life ability. This is limited in several ways:

• The cleric may choose any number of creatures within 30 feet range and divide these hit points among them.

• It cannot restore hit points above the half of the target creatures hit point maximum. (The relevant wording is:

  This feature can restore a creature to no more than half of its hit point maximum.

  This means you can restore any amount of hit points (up to 5x cleric level) as long as the current amount of hp of the target do not exceed half of the hit point maximum of the target.

• It does not work on undead or constructs

Regarding these limits:

• Example One:

  Target creatures hit points: 20/50
  The half of the maximum would be 25, so preserve life could only restore 5 hit points for this creature.

• Example Two:

  Target creatures hit points: 2/24
  The half of the maximum would be 12, so preserve life could restore 10 hit points.

Combining both examples, when both creatures are within 30 feet of the cleric he could restore 5 hit points to the first and 10 hit points to the second creature.

The multi classing rules state (PHB p164):

If you already have the Channel Divinity feature and gain a level in a class that also grants the feature, you gain the Channel Divinity effects granted by that class, but getting the feature again doesn’t give you an additional use of it.

Therefore, RAW, the character gets both the Channel Arcana uses from the Wizard class and the Channel Divinity uses from the Cleric class as they are different class features. Even though Channel Arcana allows the use of a channel divinity option it is not Channel Divinity itself.

This is clearly very powerful, a work-around the multi-class rules put in place to limit the number of channel divinity options that can be used by a single character between short rests.

The obvious house rule is to treat them both as Channel Divinity for uses under the multi-class rules, even though Channel Arcana also allows Divine Arcana which is not a technically a Channel Divinity option.

I have no experience of running such a character so this is all theoretical.