Learn Finnish: Milloin monet kerhot olivat liittyneet tähän järjestöön? - When had many clubs joined this organization?

Both mean 'many clubs', but they behave differently as subjects. Monta kerhoa is used as a quantity, typically in 'there is/are' (existential) sentences. Here, monet kerhot is the active subject performing a specific action, so we use the nominative plural for both the word 'many' (moni -> monet) and the noun.

How do we form the 'had joined' tense in olivat liittyneet?

This is the pluperfect tense, used for an action completed before another point in the past. It is built using the past tense of olla (here, olivat because the subject is plural) plus the past participle of the main verb. Because the subject is plural, liittynyt gets the plural -t marker, becoming liittyneet.

Why is the word for 'this' in the form tähän?

Demonstrative pronouns like tämä (this) must agree with the case of the noun they modify. Since the sentence uses the illative ('into') case for the organization (järjestöön), the pronoun must also take the illative case, changing tämä to tähän.

Why does järjestöön end with -ön rather than taking a normal object case?

The verb liittyä (to join) has a specific rule (called a verb rection): it requires the group being joined to be in the illative case. In Finnish, you do not just join an organization as a direct object; you attach yourself 'into' it.