How do multiclassing spell slots work?

[Flerion]

With 6 level paladin (4 level 1 slots + 2 level 2 slots) and 1 level clric (2 level 1 slots), shall I have 6 level 1 slots or do they not stack?

[The Wedge]

https://bg3.wiki/wiki/Spells#Spell_slots_per_level

[Zsrai]

Effective Caster Levels, or whatever 5e calls them, are cumulative. The full casters (Cleric, Druid, Sorc, Wizard, Bard) are... well full casters. 1x level. Paladins and Rangers are half casters, so 0.5x level. Arcane Trickers rogues and Eldritch Knight fighters are one-third casters, so 0.33x level.

Your example, of level 6 paladin + 1 cleric breaks down to:
(6 x 0.5) + (1 x 1)
(3) + (1)
4

So you effectively are a 4th level caster, which gives you four 1st level spells and three 2nd level spells.