Из‑за влажности на плитке в ванной появилось маленькое пятно, и мне пришлось тереть его губкой.

Из‑за requires the genitive case (родительный падеж).
So влажность → влажности (genitive singular).
In general: из‑за + Genitive = because of / due to (often with a slightly negative or “problem-causing” feel).

• из‑за + noun (Gen.): “because of + noun”
  → из‑за влажности = “because of the humidity”
• из‑за того, что + clause: “because (of the fact) that + sentence”
  → из‑за того, что было влажно… = “because it was humid…”

So you use из‑за with a noun phrase, and из‑за того, что with a full clause.

Because the spot is on the surface of the tile, not inside it.
Russian often uses:

• на + Prepositional for surfaces: на столе, на стене, на плитке
• в + Prepositional for being inside something: в комнате, в шкафу

So на плитке = “on the tile.”

It’s the prepositional case (предложный падеж) singular:
плитка → (на) плитке.
Many location phrases use на/в + prepositional.

В ванной uses the prepositional case and means “in the bathroom.”

Ванная here is a noun meaning “bathroom” (historically it comes from the adjective “bathroom-type,” but in modern Russian it’s commonly used as a noun).
Declension: ванная → в ванной.

Because the subject is пятно, which is neuter.
Past tense verbs agree in gender and number:

• пятно (neuter) → появилось
• дырка (feminine) → появилась
• след (masculine) → появился

Появилось is past tense of появиться (perfective).
Perfective is used for a single completed event: the spot “appeared” (came into existence) at some point.

If you used imperfective появлялось, it would suggest something like “used to appear / was appearing repeatedly,” which doesn’t fit as well here.

Adjectives agree with nouns in gender, number, and case.

Here:

• пятно is neuter singular nominative
• so маленький becomes маленькое (neuter singular nominative)

Other examples:

• маленькая точка (feminine)
• маленький след (masculine)
• маленькие пятна (plural)

This is a common Russian structure meaning “I had to / it turned out I needed to.”

• пришлось is an impersonal past form (neuter singular) of прийтись
• мне is dative: “to me” → “it fell to me / I ended up having to…”

So мне пришлось тереть… = “I had to scrub…”

After пришлось, Russian typically uses the infinitive. The choice of aspect depends on meaning:

• тереть (imperfective) focuses on the process/effort: “to scrub (for a while)”
• потереть (perfective) often means “to rub/scrub a bit” (a short, bounded action)
• оттереть (perfective) means “to scrub off successfully” (result-focused)

Here, тереть fits because it emphasizes the action/work rather than explicitly stating the result.

его is the accusative (direct object) form meaning “it/him.”
Here it refers to пятно (“spot”), which is neuter, so его = “it.”

(For a neuter noun like пятно, Russian uses оно as “it,” and его as “it” in object position.)

Because this is the “tool/instrument” meaning: with a sponge.

Russian uses the instrumental case for “by means of / with (a tool)”:

• тереть губкой = “to scrub with a sponge”

If you said губку, that would be the direct object (“scrub the sponge”), which changes the meaning.