This sentence is ambiguous as to the gender of the model and you'd have to work around it somehow to clarify the gender if that's something you need.
If you exchange sin for hans or hennes, the sentence's meaning will change to hugging someone else's mother rather than the model's own.
sin is used to point back to subjects in the third person, either singular (where you say his or hers in English) or plural, where you say their in English. If you'd say hans or hennes in Swedish here, it would not be the model's own mother, but somebody else's.
they and their in English is also used as a gender neutral pronoun in the singular, which is why their mom is an accepted answer here.
sin is a reflexive possessive pronoun which is used for the third person. This means that when he, she or they is the subject of a sentence, whatever they own is referred to with sin.
Jag tar min bok 'I take my book'
Du tar min bok 'You take your book'
Hon tar sin bok 'She takes her book'
sig is a reflexive personal pronoun, used when the subject of a sentence is also the object of the action in it
jag rakar mig 'I am shaving [myself]'
du rakar dig 'you are shaving [yourself]'
han rakar sig 'he is shaving [himself]'
sin is ambiguous, so "his" and "her" are both fine. However, there can only be one default option displayed, so the course contributors have chosen to alternate between "his" and "her" in those cases. This just happens to be one of the sentences where "his" is the default. :)