Learn Hardcore German: Ich kann mir das Fest im Garten gut vorstellen. - I can easily imagine the celebration in the garden.

The mir signals that the imagining happens in your own mind. Without mir, vorstellen usually means something else (like “to present” or “to introduce”), not “to imagine”.

So:

Ich kann mir das Fest gut vorstellen. = I can imagine the party well / easily.
Ich kann das Fest gut vorstellen. ≈ I can present the party well (very unusual sentence, and a different meaning).

Why is the reflexive pronoun mir in the dative and not mich (accusative)?

In German, reflexive pronouns can be accusative or dative, depending on the verb and the structure:

Accusative reflexive: when the person is the direct object.
- Ich wasche mich. – I wash myself.
Dative reflexive: when there is another direct object, and the reflexive refers to whom the action is done for or to.
- Ich wasche mir die Hände. – I wash my hands (for myself).

With sich etwas vorstellen (to imagine something), the thing imagined is the direct object:

das Fest = direct object (accusative)
mir = indirect / affected person (dative reflexive)

So you must say:

Ich kann mir das Fest gut vorstellen. (correct)
Not: Ich kann mich das Fest gut vorstellen. (incorrect)

Is vorstellen always reflexive when it means “to imagine”?

Yes, in the “imagine” sense it is normally reflexive with a dative pronoun:

Ich stelle mir das Fest vor. – I imagine the party.
Kannst du dir das vorstellen? – Can you imagine that?
Wir konnten es uns nicht vorstellen. – We couldn’t imagine it.

If you drop the reflexive pronoun, vorstellen usually changes to one of its other meanings:

jemanden vorstellen = to introduce someone
- Ich möchte dir meinen Freund vorstellen. – I would like to introduce my friend to you.

So to express “imagine”, keep the dative reflexive:
sich (Dat.) etwas vorstellen

Why is vorstellen split, with vor at the end? Why not keep it together?

Vorstellen is a separable prefix verb: vor- (prefix) + stellen (base verb).

In a simple main clause (no modal verb), the finite verb goes in position 2, and the prefix goes to the very end:
- Ich stelle mir das Fest vor.
With a modal verb like können, the modal is the finite verb in position 2, and the main verb goes to the end in the infinitive form. For separable verbs in the infinitive, the prefix stays attached:
- Ich kann mir das Fest gut vorstellen.
  - kann = position 2 (finite modal)
  - vorstellen = infinitive at the end (not split in the infinitive)

So:

Present, no modal: Ich stelle mir das Fest vor.
With modal: Ich kann mir das Fest vorstellen.

Why is kann in second position? Could I move it?

In a normal German main clause, the finite verb must be in position 2. That’s a core word order rule.

In your sentence:

Ich – first element
kann – finite verb (must be second)
Everything else: mir das Fest im Garten gut vorstellen

If you move another element to the front, the verb still stays second, and the subject moves after the verb:

Im Garten kann ich mir das Fest gut vorstellen.
Das Fest im Garten kann ich mir gut vorstellen.

But kann itself must remain in the second position (counting by chunks, not individual words). You cannot move it to the end or the beginning in a main clause.

What case is das Fest in? How can I tell?

Das Fest is in the accusative case as the direct object of vorstellen.

The structure is:

Ich (nominative subject)
mir (dative reflexive)
das Fest (accusative direct object)
im Garten (prepositional phrase of place)
gut (adverb)
vorstellen (main verb, infinitive)

For neuter singular nouns (like das Fest), the nominative and accusative forms are the same (das Fest), so you can’t see the case change in the article — but by function, it is the direct object, so it’s accusative.

What exactly does gut add? Does it mean “well” or “easily”?

Literally, gut means “well”.

Ich kann mir das Fest gut vorstellen.
→ I can imagine the party well.

In natural English, this is often translated more idiomatically as:

I can easily imagine the party in the garden.

So gut here expresses:

that it is no problem for you to imagine it,
that it is clear and vivid in your mind.

You can intensify it:

Ich kann mir das Fest sehr gut vorstellen. – I can very easily / very well imagine the party.

Could I leave out gut and just say Ich kann mir das Fest im Garten vorstellen?

Yes, that is perfectly grammatical:

Ich kann mir das Fest im Garten vorstellen.
= I can imagine the party in the garden.

Without gut, the sentence is a bit more neutral. With gut, you emphasize that you can imagine it clearly / easily / vividly.

Both are correct; it’s just a difference in nuance.

Why is it im Garten and not in dem Garten?

Im is simply the standard contraction of:

in + dem → im

So:

in dem Garten = in the garden
im Garten = in the garden (more usual in speech and writing)

The full form in dem Garten is also grammatically correct but sounds more formal or emphatic. In everyday language, people almost always say im Garten.

Why is it in + dem Garten (dative) and not in + den Garten (accusative)?

The preposition in can take either dative or accusative, depending on the meaning:

Dative = location (where?)
Accusative = direction (into where?)

In your sentence, the garden is a location, not a direction of movement:

Wo? (Where?) – im Garten → dative (in dem Garten)

Compare:

Wir sitzen im Garten. – We’re sitting in the garden. (dative: location)
Wir gehen in den Garten. – We’re going into the garden. (accusative: movement towards)

So im Garten (dative) is correct here.

Can I change the word order of im Garten and gut? For example:
Ich kann mir das Fest gut im Garten vorstellen.

Yes, that word order is also possible:

Ich kann mir das Fest gut im Garten vorstellen.
Ich kann mir das Fest im Garten gut vorstellen.

Both are grammatically fine. The difference is subtle:

… das Fest im Garten gut vorstellen.
Slightly stronger grouping of “the party in the garden” as one mental image that you can imagine well.
… das Fest gut im Garten vorstellen.
Slightly more emphasis on the idea that the garden is a good / fitting place in which you can imagine the party.

In normal conversation, most natives would probably say … das Fest im Garten gut vorstellen. as in your original sentence.

How would this look in a simple past sentence without a modal verb?

Without the modal können, you use vorstellen as the main verb, and it splits again:

Present:

Ich stelle mir das Fest im Garten gut vor.

Simple past:

Ich stellte mir das Fest im Garten gut vor. (formal/written style)

In everyday spoken German, people would usually use Perfekt (present perfect) instead of simple past for this verb:

Ich habe mir das Fest im Garten gut vorgestellt.

Can I say Ich kann es mir gut vorstellen, das Fest im Garten like in English “I can imagine it, the party in the garden”?

You can say:

Ich kann es mir gut vorstellen. – I can easily imagine it.

But if you already name das Fest im Garten, you usually don’t use an extra “es”:

Ich kann mir das Fest im Garten gut vorstellen. ✅ (normal, natural)
Ich kann es mir, das Fest im Garten, gut vorstellen. ❌ (sounds odd and overloaded)

In German, you typically choose either the pronoun (es) or the full noun phrase (das Fest im Garten), not both at the same time in this kind of sentence.