Learn Hardcore Finnish: Eilen jouduin peruuttamaan ajan, mutta tänään käynti onnistui. - Yesterday I had to cancel the appointment, but today the visit worked out.

Finnish usually drops subject pronouns because the verb ending already shows the person/number.
jouduin = I ended up / I had to (1st person singular, past tense).
So (minä) jouduin is grammatical, but minä is normally omitted unless you want emphasis/contrast.

What exactly does jouduin mean here, and how is it different from piti?

joutua means something like to end up having to, often with a sense that it was unavoidable or not what you wanted.
So Eilen jouduin peruuttamaan... suggests: “Yesterday I ended up having to cancel...” (maybe due to circumstances).

piti (minun piti) is more neutral: I had to / I was supposed to, and it can sound more like obligation or plan than “unfortunate necessity.”

Why is joudun changed to jouduin?

jouduin is the imperfect (simple past) form of joutua:

present: joudun = I end up / I have to (now)
past: jouduin = I ended up having to / I had to (yesterday)

The -in ending marks 1st person singular in the past tense for many verbs.

Why do we say jouduin peruuttamaan instead of jouduin peruuttaa?

After joutua, Finnish commonly uses the 3rd infinitive illative: -maan / -mään, which expresses “into doing / to do (as a resulting necessity).”

So:

jouduin peruuttamaan = I ended up having to cancel
peruuttamaan is the 3rd infinitive illative of peruuttaa.

Using the basic dictionary form (peruuttaa) after jouduin is not the normal pattern.

What grammatical form is peruuttamaan exactly?

It’s the 3rd infinitive illative:

base verb: peruuttaa (to cancel / to back up)
3rd infinitive stem: peruutta- + ma
illative: peruuttamaan (“into cancelling” → “to cancel” in this construction)

This form is very common after verbs like mennä (go), tulla (come), jäädä (stay), päästä (get to), joutua (end up having to).

Does aika mean “time” or “appointment” here?

Here ajan means an appointment slot / a booked time, so in natural English you’d translate it as the appointment or my appointment.

Finnish often uses aika for an appointment time, especially in healthcare and services:

varata aika = to book an appointment
peruuttaa aika = to cancel an appointment

Why is it ajan (not aika)? What case is that?

ajan is the genitive (also used as the total object form in many past-tense sentences).

With many verbs, Finnish chooses:

total object (completed/whole action) → often genitive in the past: peruutin ajan / jouduin peruuttamaan ajan
partial object (incomplete/ongoing/indefinite amount) → partitive

Canceling an appointment is typically seen as a complete, one-time action, so ajan fits well.

Could it also be peruuttamaan aikaa with partitive?

In this specific “appointment” meaning, peruuttaa aikaa is usually not what you want, because aikaa strongly reads as literal “time (some amount of time).”
So peruuttaa ajan = cancel an appointment, while peruuttaa aikaa would more likely be interpreted as something like “cancel time” (odd) or would require a special context.

If you mean “cancel the appointment booking,” you might also see peruuttaa ajanvaraus.

What does käynti mean, and why is it used instead of a verb like “go”?

käynti is a noun meaning a visit (often a scheduled visit, e.g., to a doctor, office, etc.).
So tänään käynti onnistui is literally today the visit succeeded, meaning today the visit worked out / happened successfully.

Finnish often uses a noun like käynti where English might use a verb phrase like “the visit went well” or “I was able to go.”

Why is it onnistui and not something like onnistunut?

onnistui is the past tense verb (imperfect) of onnistua: “succeeded / worked out.”
onnistunut is a past participle meaning “successful” or “having succeeded,” and it would need a different structure, e.g.:

Käynti oli onnistunut. = The visit had been successful.

In your sentence, the simple past onnistui is the natural choice.

What is the subject in tänään käynti onnistui?

The subject is käynti (the visit) in the nominative case.
The verb onnistui is 3rd person singular to match: käynti onnistui = the visit succeeded / worked out.

Can I change the word order, like Tänään onnistui käynti?

Yes, Finnish word order is flexible and is often used to control emphasis/topic. For example:

Tänään käynti onnistui. (neutral: “Today, the visit worked out.”)
Tänään onnistui käynti. (more like: “Today, the one that worked out was the visit.”)

The original order is very natural and straightforward.

Why is there a comma before mutta?

In Finnish, you generally put a comma between two independent clauses joined by a coordinating conjunction like mutta (but):

Eilen jouduin peruuttamaan ajan, mutta tänään käynti onnistui.

Each side could stand as its own sentence, so the comma is standard.