"He likes his cabin."
Translation:Han liker hytta si.
'hytte' is a feminine noun, which, like all feminine nouns, can be inflected as a masculine noun.
'hytta(feminine)' = 'hytten(masculine)'
'si' is used for feminine nouns, while 'sin' is used for masculine (and 'sitt' for neuter and 'sine' for plural).
So you can either say "hytta si" or "hytten sin".
Except for the neuter form, 'huset sitt', which has a suffix that's just as long as the masculine form, but the possessive is as long as the plural 'husene sine'.
I think it would be easier to remember that the last part of the possessive contains the same letter as the suffix. 'huset sitt', 'husene sine', 'hytten sin', and the feminine form is the only one ending in a vowel: 'hytta si'.
sine are related in that they all point back to the subject as the possessor, but they're not completely interchangeable.
Which word is correct to use depends on the grammatical gender and number (singular or plural) of the object of possession.
In this case,
hytta is a singular noun that has been declined as feminine, which means you have to use the corresponding singular feminine possessive
si, not the singular neuter possessive
hytta si (in addition to
si(n) hytte and
hytten sin) is correct.