It needs to be changed to, “... am available anytime this Tuesday, June 25th or Wednesday, the 26th."

Greg is correct. Or you could say...am available Tuesday or Wednesday, June 25th and (June) 26th. (June is optional).

There are a few ways you could write this sentence. 1. "I am available any time this Tuesday, June 25th, and Wednesday, June 26th.". 2. "I am available any time this Tuesday (June 25th) and Wednesday (June 26th). 3. "I am available any time on June 25th (Tuesday) and June 26th (Wednesday). 4. "I am available any time this Tuesday and Wednesday." (You used "THIS"- "...this Tuesday", which already implies that you are talking about the Tuesday and Wednesday specifically coming up in this week, so the date is not necessarily needed because we already know which Tuesday and Wednesday you are referring to). I hope this is clear 😊