"Fyddwch chi gartre yfory?"
Translation:Will you be at home tomorrow?
'Home', 'homewards', 'at home' tend to get confused. And the -f endings in Welsh are frequently only lightly pronounced or omitted altogether in colloquial Welsh:
- cartre(f) - home
- gartre(f) - at home (cartref as an adverb, so mutated)
- adre(f) - homewards (from an older tua thref - 'towards home', in a time when tref meant 'home/homestead' rather than 'town' as it does nowadays.)
In some dialects adre(f) is used informally in place of gartre(f) for 'at home', but not in more formal usage. In some dialects some people still use the older tua thre, pronounced /sha/ thre for adre(f).
cartref can also be used in the sense of 'home-made', as in cyffug cartref - 'home-made fudge'
Yes, the interrogative particle a is not generally used in colloquial Welsh, but its 'ghost' is what causes the soft mutation of the question forms of verbs.
(The word a has other meanings and uses in Welsh - you will have already met a/ac meaning 'and' and there are a couple of others as well.)