The University Preparatory Programme is an adult education program, so you need to apply for an “other type” visa. This type of visa/residence permit does not allow you to work. Employment is not recommended due to the high number of lessons.
You will also find information about entering Hungary and visa on the following pages:
Visa-free travel to Hungary: https://konzinfo.mfa.gov.hu/en/visa-free-travel-hungary
How to Apply for a Visa: https://konzinfo.mfa.gov.hu/en/how-apply-visa
EU Visa Facilitation Agreements: https://konzinfo.mfa.gov.hu/en/eu-visa-facilitation-agreements
List of Third Countries Where a Schengen State Issues Visas on Behalf of Hungary: https://konzinfo.mfa.gov.hu/en/list-third-countries-where-schengen-state-issues-visas-behalf-hungary