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Eu - Their
eu....(nhw) their, them
sample sentence: Maen nhw'n dathlu eu diwrnod sant cenedlaethol (nhw). - They are celebrating their national saints day.
Image: Dydd Gwyl Dewi Sant
fy, '(y)n....(i) - my
dy....(di) - your (singular)
ei....(e/o/fe) - his
ei....(hi) - her
ein....(ni) - our
eich....(chi) - your (plural)
eu....(nhw) - their
You will frequently come across this construction in both the written and spoken languages. The appropriate personal pronoun is added after the noun in order to reinforce or underline the person of the possessor. The addition of the pronoun is not. however, mandatory and the above example sentence works equally well without it.
The best likely explanation of the origin of this practice can be found in Gareth King's Modern Welsh: A Comprehensive Grammar
' The practice of 'echoing' the pronoun of the possessor after the thing possessed is widespread and may have arisen from the fact that ei (his or her) and eu (their) sound the same.'
Clearly this could lead to some confusion since you would not be able to tell his , her and their apart, unless, as in some cases the following noun is subject to mutation.