This or the

Hi teachers, may I ask about the proper usage of this and the in my given example below? I wonder which one of them is more correct.

Greetings!

I am a student of Bachelor of Industrial Technology as confirmed by the Office of the University Registrar. To complete the requirements of the program, I need to enroll PE 10 Physical Education 1 in Special basis because I failed the/this subject.

I am therefore, respectfully requesting your good office to allow me to enroll the above-mentioned subject/s.

I am hoping that my request merits your kind consideration and favorable action.

Thank you.