Simply stated, you cannot.
When your father originally exited the US, if he had a paper-copy I-94 and failed to properly turn it in at that time, there are procedures he could follow including mailing it to a specific address, along with corroborating information, to get his records updated.
However, if he did properly turn it in when exiting the US via an International flight home, there are no provisions for verifying that your records were properly updated. Many people have complained in various forums that there are many reasons the I-94 may get lost from the time it's handed over to the database update, none of which are the fault of the person who would then be accused of over-staying. Still, there is no way to check, other than attempting to apply for a new visa and/or enter the country if allowed visa-free.
If you and your father are truly worried, take what documentation you may still have showing he departed the country on time with you. That is, unfortunately, all you can do at this time.