Date stored as varchar
or TEXT
makes life miserable so better to store as date
or datetime
data type.
In your case you need to use str_to_date()
for conversion before doing any format
$query = "SELECT
Event_Title,
Event_Details,
Event_Time,
Event_ID,
date_format(str_to_date(Start_Date,'%m/%d/%Y'),'%m/%d/%Y') as Start_Date
FROM tevents
ORDER by date_format(str_to_date(Start_Date,'%m/%d/%Y'),'%Y-%m-%d') DESC";
If its just for ordering then no need to do the
date_format(str_to_date(Start_Date,'%m/%d/%Y'),'%m/%d/%Y') as Start_Date
You can directly select since its converting to the same format, for ordering its needed.