It's possible. Just use two prepared queries.
$stmt = $dblink->prepare("INSERT INTO images
(project_id, user_id, image_name, date_created, link_to_file, link_to_thumbnail, given_name)
VALUES (?,?,?,?,?,?,?)");
$stmt->bind_param("ssssss", $project_id, $user_id, $image_name, $date_created, $link_to_file, $thumbnail, $ImageName);
$stmt->execute();
$stmt = $dblink->prepare("INSERT INTO images_history
(project_id, user_id, image_name, date_created, link_to_file, link_to_thumbnail, given_name, day, month, year)
VALUES (?,?,?,?,?,?,?,?,?,?)");
$stmt->bind_param("ssssssssss", $project_id, $user_id, $image_name, $date_created, $link_to_file, $thumbnail, $ImageName, $day, $month, $year);
$stmt->execute();
It is not only much cleaner but also 100% safe from SQL injection.
And if one of your queries fails, simply ask mysqli for the error message and then fix the error.
Some answers on Stack Overflow are so self-contradicting that it's just mind-blowing.
The key is that you must use mysqli_multi_query if you want to execute more than one query in a single call. For security reasons, mysqli_query will not execute multiple queries to prevent SQL injections.
It basically says, "The key is that you must use a firearm without a safety catch, because a regular weapon won't let you shoot yourself in the foot. So here is the way to break it down and now you can cripple yourself in a single shot!"
Despite the fact the OP didn't ask how to run two queries in a single call, despite citing the explicit warning that the ability to run multiple queries in a single call is inherently dangerous, the answer nonchalantly provides the way to circumvent this limitation.
The worst part, all this dangerous and toilsome mess is for naught. Simply because there is not a single reason to run several queries in a single call. Running queries one by one is how a database API is meant to be used.