sHE LIKES HER TEA WITH cows milk
Uthanda iti yakhe nobisi lwenkomo: she likes her tea with cow's milk
ukuthanda: to like/love
Here we can see the possessive for the 3rd person, as in he or she.
This is 'akhe'
It becomes yakhe essentially because we are talking about 'iti' which begins with a I/yi sound. So it would be the same for his meat (inyama yake) or her house (indlu yakhe).
If we were talking about a guitar (isigingci) it would be isigingci sakhe.
or dogs (izinja) it would be izinja zakhe.
Remember, if you are talking about 'yours' it is akho (like izinja zakhe) and for mine it is 'am (or izinja zam)
You can also see a similar effect with the milk in this line as ubisi (milk) carries the prefix 'lw' with it, so milk of the cow is not inkomo, but lwenkomo.
There are actually 15 different noun groups that require you to remember the different prefixes for groups.
This sounds kind of scary but actually once you can speak the basics of isiXhosa it is largely intuitive and you'll only have to occasionally check with the noun groups.
Try not to confuse ubisi (milk) with ubusi (honey). Although it must sound good in the Xhosa bible talking about the land of milk and honey : umhlaba wobusi nebisi.