Well, you are learning ... the hard way ... what doesn't work.
The only thing the backup of the moodle 4.3.2 code they gave you is to see what additonal addon folders you can find ... mod/block/theme/quiz question types.
With only a 3.8.1 sql dump to work with that is key ... and the determining factor on how you approach this.
That dump is imported into a DB.
You have to acquire 3.8.x code and then manually setup config.php from config-dist.php
Copy config-dist.php to config.php - change config.php for type of DB (mariadb), DB user, DB password, location of the 4.3.x moodledata directory (which no longer matches files moodle 3.8.1 mdl_files tables knows about (probably have orphaned files in moodledata/filedir/ - exist there, but no reference in mdl_files table.
With the compatible PHP version + extensions in place, use the command line to upgrade.
In admin/cli/ there is a upgrade.php ....
cd /path/to/moodlecode/
php admin/cli/upgrade.php
That does not require you to login to the moodle - and that is another item ... did they give you the admin credentials? - login/password?
If not, then you'll have to pick a user that exist in mdl_users table that has a manual authentication, and change password via admin/cli/reset_password.php
If that was an admin level user login to the moodle and you should see a site admin menu.
If that user was not an admin level user, you have to log out and in config.php add a line:
$CFG->siteadmins='2,ID# of that user login whose password you changed';
Attempt login again.
If you get that far you can now see what plugins are missing from disk and install those - don't copy from the 4.2.x code you have ... acquire a compat version from
Moodle plugins site.
Now you can check the site for function - links to *some* files predict will be broken - only way to fix is to re-
upload.
Once site functions ok, now you can begin the march of the moodle.
Go to Site Admin -> Environment check -> update component.
Then use the drop down moodle version list selecting each higher version of moodle to see what that says you need.
When/IF you finish ... you'll still have a semi-broken site when it comes to orphaned files that are present in moodledata/filedir/ but not known to db mdl_files table.
Can't fix that!
Best of luck!
'SoS', Ken