Fóturinn hennar er þreyttur eftir langan göngutúr heim.

In Icelandic, the neutral and most common way to say “X’s [body part / possession]” is:

• [noun] + [definite article] + [possessor in genitive]
  → fóturinn hennar = “the foot of her / her foot”

Putting hennar before the noun (hennar fótur) is possible but sounds marked, with extra emphasis or contrast:

• Hennar fótur er þreyttur, ekki minn.
  “Her foot is tired, not mine.”

So:

• fóturinn hennar = ordinary “her foot”
• hennar fótur = “her foot (as opposed to someone else’s foot)”

The ending -inn is the definite article (“the”) attached to the end of the noun.

• fótur = “foot”
• fóturinn = “the foot”

Icelandic usually attaches the definite article to the noun, instead of using a separate word like English the.

So Fóturinn hennar literally is “the foot of her” → “her foot”.

In Icelandic, adjectives agree with the noun they describe in:

• gender (masculine / feminine / neuter)
• number (singular / plural)
• case (nominative / accusative / dative / genitive)

Here:

• fóturinn is masculine, singular, nominative (subject of the sentence).
• Therefore, þreyttur is also masculine singular nominative.

If the noun changed, the adjective would change:

• Fóturinn er þreyttur. – The (masc.) foot is tired.
• Hendin er þreytt. – The (fem.) hand is tired.
• Augað er þreytt. – The (neut.) eye is tired.

þreyttur / þreytt / þreytt are all “tired”, but they change form to match the noun.

Eftir is a preposition that (among other things) means “after” in a temporal sense.

When eftir means “after (a period of time or an event)”, it typically governs the accusative case. That is what we have here:

• eftir langan göngutúr
  
  • langan = masculine singular accusative of langur (“long”)
  • göngutúr = masculine singular accusative (“walk”)

So the phrase means “after a long walk (home)” and eftir is the reason langur becomes langan.

Because eftir requires accusative here, and the adjective must agree in case with the noun.

Base forms:

• Adjective: langur – “long” (masc. nom. sg.)
• Noun: göngutúr – “walk” (masc. nom./acc. sg.)

In the accusative masculine singular, langur becomes langan:

• Nominative: langur göngutúr – “a long walk” (as subject)
• Accusative: eftir langan göngutúr – “after a long walk”

So langur → langan because of the accusative case governed by eftir.

Göngutúr is a compound noun:

• ganga – “a walk, walking”
• túr – “trip, tour”

Literally: a “walking-trip”, i.e. a walk / a stroll.

Grammar:

• Gender: masculine
• Typical singular forms:
  
  • Nominative: göngutúr
  • Accusative: göngutúr
  • Dative: göngutúr
  • Genitive: göngutúrs

In the sentence, it is masculine accusative singular in eftir langan göngutúr.

Heim and heima are both related to “home”, but they are used differently:

• heim = “home(wards)”, direction (going/moving to home)

  • Ég fer heim. – “I am going home.”
  • eftir langan göngutúr heim – “after a long walk home (towards home)”

• heima = “at home”, location (staying at home)

  • Ég er heima. – “I am at home.”
  • Hún var heima eftir göngutúrinn. – “She was at home after the walk.”

In the sentence, heim says that the walk was towards home, not just any walk.

• Fóturinn hennar er eftir langan göngutúr þreyttur

  • This sounds unnatural in ordinary Icelandic. Predicative adjectives (þreyttur) almost always come right after the verb er (“is”).
  • So er þreyttur eftir … is the normal order.

• Hennar fótur er þreyttur eftir langan göngutúr heim

  • Grammatically possible, but it sounds marked / contrastive, as if you are emphasizing her as opposed to someone else:
    
    • “Her foot is tired after a long walk home (not his / not mine).”
  • The neutral, everyday word order is Fóturinn hennar er þreyttur ….

So the original sentence is the natural, unmarked word order.

Replace hennar (“her”) with minn (“my”):

• Fóturinn minn er þreyttur eftir langan göngutúr heim.

Notes:

• fóturinn stays the same (masc. sg. definite).
• minn follows the usual pattern [noun] + [definite article] + [possessive after it].
• Everything else (cases, endings) stays exactly as in the original sentence.

Yes, hennar is the genitive of “hún” and is used for a female person (or grammatically feminine referent):

• fóturinn hennar – “her foot” (belonging to a woman / feminine person)

Other third‑person possessives of this same type:

• hans – “his” (belonging to a man)
  
  • fóturinn hans – “his foot”
• þeirra – “their” (belonging to them, any gender)
  
  • fóturinn þeirra – “their foot”

So you get:

• Fóturinn hans er þreyttur … – “His foot is tired …”
• Fóturinn þeirra er þreyttur … – “Their foot is tired …”