Your sql is wrong. Apart from the gaping wide open SQL injection attack vulnerability, you’re generating bad sql.
e.g. consider submitting “Fred” as the first name:
$First_Name2 = "Fred";
$query = "UPDATE people SET Fred = First_name WHERE ....";
now you’re telling the db to update a field name “Fred” to the value in the “First_Name” field. Your values must be quoted, and reversed:
$query = "UPDATE people SET First_name="$First_Name2" ...";
You are also mixing the mysqli and mysql DB libraries like a drunk staggering down the street. PHP’s db libraries and function/method calls are NOT interchangeable like that.
In short, this code is pure cargo-cult programming.
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solved PHP script to update mySQL database