I was working 24 hours a week that was 8 hours Monday, Thurs and Frid with 12 days annual leave. I now work 24 hours the same but 6 hours a day over 4 days - is my holiday entitlement the same?
No - it should increase to 16 days (calculated as 12*8/6). However it might end up being a little different than this, depending how your organisation deals with Bank Holidays and part-timers.
All employees -including part-time workers- are entitled to four weeks' holiday. In your case, yir normal working week was three days so four weeks' leave was 4 x 3 = 12 days. Now yir normal week is four days so that now means the entitlement is 4 x 4 = 16 days. The Bank Holidays can be included in the entitlement and not in addition to it if the Employer wants.