Your cleric level and the cleric table tells you how many cleric cantrips you can know, and likewise your artificer level and the artificer table tells you the number of artificer cantrips you can know.
One of the major benefits of multi-classing is knowing a lot of cantrips and more spells than normal. Typically these choices can be carefully made so as to maximize useful spells. Usually you only want a few levels of one class, so be sure to pick the right spells for the rest of your career before you stop advancing
When you multiclass, you refer to the multiclass spell slot chart to determine your spell slots. But you determine your spells known and prepared individually for each class. One example of this is a 6/14 artificer-cleric, who, despite having 9th level spell slots, doesn't know any 9th or 8th level spells. You choose cleric spells as though you were a 14th level cleric, and artificer spells as though you were a 6th level artificer. This applies to cantrips as well.
NOTABLE EXCEPTION: Cantrips level based on character level, not on spellcasting level. (The power of the cantrips, not the number of them.)
I have a Q: I'm Multiclassing an Artificer 2 with Cleric 1, how many cantrips do I get?
5 from those class levels.
2 Artificer cantrips, 3 Cleric cantrips.
Helpful rewriter of Japanese->English translation and delver into software codebases (she/e/they)
Your cleric level and the cleric table tells you how many cleric cantrips you can know, and likewise your artificer level and the artificer table tells you the number of artificer cantrips you can know.
One of the major benefits of multi-classing is knowing a lot of cantrips and more spells than normal. Typically these choices can be carefully made so as to maximize useful spells. Usually you only want a few levels of one class, so be sure to pick the right spells for the rest of your career before you stop advancing
When you multiclass, you refer to the multiclass spell slot chart to determine your spell slots. But you determine your spells known and prepared individually for each class. One example of this is a 6/14 artificer-cleric, who, despite having 9th level spell slots, doesn't know any 9th or 8th level spells. You choose cleric spells as though you were a 14th level cleric, and artificer spells as though you were a 6th level artificer. This applies to cantrips as well.
NOTABLE EXCEPTION: Cantrips level based on character level, not on spellcasting level. (The power of the cantrips, not the number of them.)