Change the voice: Mona was writing a letter to her father.

A letter has been written to her father by Mona.

A letter was being written to her father by Mona.

A letter had been written to her father by Mona.

None of these

A letter was being written to her father by Mona.

The sentence is in past continuous tense: was writing.

In passive voice, past continuous becomes was being + past participle → was being written.