You use the best progression from your two classes. Player's Handbook, "Multi-CLass Benefits and Restrictions", page 44, last paragraph before the multi-classing example:
If the optional proficiency system is used, the character […] gains new proficiency slots at the fastest of the given rates.
which is reiterated on page 52, end of the first full paragraph:
Multi-class characters can use the most beneficial line on Table 34 to determine their initial proficiencies and when they gain new proficiencies.
You apply this progression as you gain levels, which ends up meaning that it applies to both classes separately. Your Cleric 8 / Thief 9 should have gained 1/4 × 8 = 2 weapon proficiencies† and 1/3 × 8 = 2 NWPs (rounded down) from cleric advancement since 1st level; plus 1/4 × 9 = 2 weapon proficiencies (rounded down) and 1/3 × 9 = 3 NWPs from thief advancement since 1st level; for a total of 4 WPs and 5 NWPs gained since 1st level.
A common interpretation of the multi-classing rules is that you must fill each weapon and non-weapon proficiency slot according to the restrictions of the class level that earned it; consult with your DM to see how they handle this. Regardless of that, see the notes on multi-class priest weapon usage restrictions on page 45 of the Player's Handbook before you choose any thief weapon proficiencies that you might not be able to use.
† Though one might expect this should be multiplied by level − 1 (not the full number of levels) since you already get stuff at 1st level, the rules are more generous and grant new proficiencies at each level divisible by the rate. See PHB p. 50, "# Levels" (centre column, 3rd paragraph).
