Good idea to look up interactions but best to call your pharmacy or dr and use the other resources for "guidance only" as you await to hear from your medical professional.
Cheryl
WELCOME TO THE COMMUNITY
Phentermine does not list thyroid meds or thyroid disease as a caution or a contra-indication, so it should be alright.
You don't want to take ANY drugs or vitamins or supplements at the same time as you take your Synthroid.
Take your Synthroid with a glass of water in the morning. No food or anything for an hour. Coffee is ok, cream or milk is a major no-no.
Some meds or supplements should be spaced several hours later.
You can look up drug interactions here;
https://online.epocrates.com/public/portkey/