'r is a form of the definite article after a vowel.
The full form of this sentence is 'Dw i'n hoffi y caffi yma'
Hoffi ends in a vowel and is followed by 'Y' another vowel in Welsh.
This contracts to 'hoffi'r'
Which gives us - Dw i'n hoffi'r caffi yma
The literal translation of this sentence is 'I like the café here'
We generally translate 'the café here' as 'this café'
You may have noticed that 'caffi yma' is also two vowels next to each other and in fact we often write this sentence as:-
Dw i'n hoffi'r caffi 'ma.
But we didn't have 'ma to use to create the sentence for the course.