The multiclass spellcasting rules are more specific and override the individual class's spellcasting rules.
You determine what spells you know and can prepare for each class individually, as if you were a single-classed member of that class.
The example given in that section is a ranger 4/wizard 3. This character knows 3 1st-level ranger spells (as a 4th-level ranger) and has a spellbook with 1st- and 2nd-level wizard spells, of which he can prepare 3 plus his Intelligence modifier (as a 3rd-level wizard).
This example character has 2 3rd-level spell slots, but has no access to 3rd-level spells. He can use those slots to cast 1st- and 2nd-level spells he knows and has prepared, some of which will benefit from the increased level.
Thus, a cleric 14/paladin 6 prepares cleric spells as a 14th-level cleric and paladin spells as a 6th-level paladin.
A 14th-level cleric only has spell slots up to 7th level, meaning you can prepare 14 + Wisdom modifier cleric spells of 7th level and lower.
A 6th-level paladin has spell slots up to 2nd level, so you can prepare 3 + Charisma modifier paladin spells of 2nd level and lower.
Here is a tweet from 5e designer Jeremy Crawford validating this interpretation.