The number of sick days an employee takes per year is believed to be about 12.
The mean purpose of null hypothesis is to verify or disprove the proposed statistical assumptions, also is usually associated with just ‘equals to’ sign as a null hypothesis can either be accepted or rejected.
If you wish to test the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the null hypothesis is "the mean number of sick days an employee takes per year is equal to 12 days".
Then, the correct null hypothesis is:
[tex]H_0\colon\mu=12\text{ days}[/tex]The alternative hypothesis is an alternative to the null hypothesis, then if you want to check the claim that mean number of sick days an employee takes per year is not equal to 12 days, then the alternative hypothesis is "mean number of sick days an employee takes per year is not equal to 12 days".
Then, the correct alternative hypothesis is:
[tex]H_a\colon\mu\ne12\text{ days}[/tex]