The answer to your question depends on what he was convicted of. Sex crimes and violent crimes have different credits than ordinary crimes. It also may depend on when the crime was committed if it was before 2011. When you say that he has been in jail for 10 months, and has 416 days credit, that strongly implies that he is not eligible for half-time credits (the standard) for some reason. More information is needed to give a full answer.
You don't give us enough information to answer this question. I don't know if you're saying he got three and a half years or three years at half time. The credits you list - 10 months in custody, but with 416 days credits - don't match up.
We would need to know the EXACT charge he was convicted of, any special allegations or enhancements in the case and his record, including any priors he admitted to.
Unless you have the specifics, nobody can answer your question. His attorney should be able to though.
The above answer is for general information only and is based on the information you posted. Every case is fact dependent, so to get a thorough analysis of your situation, you will need to consult face to face with an attorney licensed to practice in the jurisdiction where the incident took place. Do not conclusively rely on any information posted online when deciding what to do about your case.
This cannot be answered without knowing the crime he was convicted of. Who told you his credits were 416 days? If he has been in for 300 days (about 10 months) he should either have credits of 600 days if it is not a violent or serious felony (300 plus 300 Good Time Work Time credits) or 345 (300 plus 15% GTWT credits of 45 days) if it was a non-serious felony. His attorney who was present at the sentencing should have the answer. The crime will also tell you if he will do the time in county jail or in state prison.