(Oops, my text got mixed up. This is what I meant to write:) If the word sounds like it starts with a vowel we put 'an' before it; if it sounds like it starts with a consonant we put 'a' before it: H When the h is pronounced (thus the sound of a consonant sound starts the word), we put 'a' before it, like 'a half'. When the h is not pronounced, thus the word sounds like it starts with a vowel, we put 'an' before it, like 'an hour'. U When the u is pronounced as a y (as a consonant) we put 'a' before it, like 'a university'. When the u is pronounced as a vowel we put 'an' before it, like 'an ulcer'

A half day leave is more correct. An is only placed before words that start with vowels such as: An open day, an awesome day, an interesting day. "A half a day of leave" or "a half day of leave" are more complete ways to say the same thing.

When the h is pronounced (thus the sound of a consonant sound starts the word), we put 'a' before it, like 'a half'. If the word sounds like it starts with a vowel we put 'an' before it; if it sounds like it starts with a consonant we put 'a' before it: H When the h is not pronounced, thus the word sounds like it starts with a vowel, we put 'an' before it, like 'an hour'. U When the u is pronounced as a y (as a consonant) we put 'a' before it, like 'a university'. When the u is pronounced as a vowel we put 'an' before it, like 'an ulcer'