I juni tar jeg fri, så jeg kan slappe av hjemme.

For months in Norwegian, the normal preposition is i: i juni, i desember, etc.

• i juni = “in June” (time period inside that month)
• på is more typical for days/parts of days or more “surface-like” time expressions (e.g., på mandag, på kvelden).
• om often means “in (about)” for future time from now, or “around/at” in some set phrases (e.g., om en uke = “in a week”).

Because Norwegian follows the V2 rule in main clauses: the finite verb must be in the second position.
Here, I juni is placed first (position 1), so the verb tar must come next (position 2), and then the subject jeg comes after:

• I juni (1) + tar (2) + jeg
  • fri
    If you start with the subject, you get the more neutral order:
• Jeg tar fri i juni.

Yes, it’s a very common expression meaning to take time off / take leave. Literally it’s “take free (time)”.
You’ll see it in several forms:

• Jeg tar fri = I’m taking time off
• Jeg har fri = I have the day off / I’m off
• Jeg tok fri = I took time off
  You can also specify how long:
• Jeg tar fri en uke. = I’m taking a week off.

Because så here links two clauses and works like so / so that. The comma marks the boundary between: 1) the main clause: I juni tar jeg fri,
2) the following clause: så jeg kan slappe av hjemme.
In Norwegian it’s normal to use a comma when connecting clauses like this.

In this sentence, så means so / so that (as a result).
Norwegian så can also mean then, especially in sequences (e.g., Først spiser vi, så går vi = “First we eat, then we go”).
Here it’s expressing purpose/result: taking time off so that you can relax.

Norwegian commonly uses kan (“can / be able to”) to express the idea of having the opportunity to do something:

• så jeg kan slappe av = “so I can relax” / “so I’ll be able to relax”
  Even if it refers to the future, Norwegian often keeps present tense after time expressions and in many future contexts. The future meaning comes from context (In June).

Both can be correct, but they mean slightly different things and are used in different structures.

1) ..., så jeg kan slappe av hjemme.
This is a clause introduced by så meaning “so that / so (that)”. It behaves like a normal clause: subject jeg comes before the verb kan.

2) ..., så kan jeg slappe av hjemme.
This is more like “..., and then I can relax at home” or “..., so I can relax at home” with så acting more like an adverb/connector, and then it becomes a main clause with V2 word order (kan second).

In short:

• så jeg kan ... = “so that I can ...” (very purpose/result-like)
• så kan jeg ... = often “then I can ... / so I can ...” with a more main-clause feel

It’s a common Norwegian phrasal verb: å slappe av = “to relax”.

• slappe is the verb, and av is a particle that belongs with it.
  In different sentences, the particle can sometimes move in certain constructions, but the safest learning approach is to treat slappe av as a unit:
• Jeg slapper av hjemme. = I relax at home.
• Jeg vil slappe av. = I want to relax.

hjemme means at home (location), while hjem means (to) home (direction/movement).

• slappe av hjemme = relax at home (no movement)
• dra hjem = go home (movement toward home)

Yes, but the meaning changes slightly.

• ta fri is general: taking time off (a day, a week, unpaid/paid—context decides).
• ta ferie specifically means going on holiday/vacation (often longer and more “vacation-like”).

So:

• I juni tar jeg fri = In June I’m taking time off.
• I juni tar jeg ferie = In June I’m taking vacation.

Month names in Norwegian typically don’t take endings in this kind of time expression. You simply say:

• i juni, i juli, i august
  No definite form is used here because you mean the time period “in June” generally, not “in the June (that we’ve already mentioned)” as a noun phrase.

A rough pronunciation guide (varies by dialect):

• I juni: ee YOO-nee (the j is like English y)
• tar jeg fri: tahr yai free (many dialects pronounce jeg like yai or jæi)
• så jeg kan slappe av hjemme: so yai kahn SLAH-peh av HEM-meh

Key points:

• j in juni sounds like y.
• slappe has a short a sound (like “ah”), and double consonants usually signal a short vowel.
• hjemme starts with hj-, which many speakers pronounce close to just y- or a softened h+y sound depending on dialect.