The correct answer is A. was.
The sentence “When my uncle entered the house, I was writing a letter” is in the simple past tense. This means that the action of writing the letter was happening at a specific point in time in the past. The other options are not in the simple past tense.
Option B, would be, is in the conditional tense. This tense is used to talk about things that might happen in the future, or things that are possible but not certain. In this case, it would not make sense to say that I might be writing a letter when my uncle entered the house, because I was actually writing a letter.
Option C, had been, is in the past perfect tense. This tense is used to talk about things that happened before another event in the past. In this case, it would not make sense to say that I had been writing a letter before my uncle entered the house, because I was actually writing a letter when he entered.
Option D, should be, is in the modal verb should. This verb is used to talk about things that are necessary or advisable. In this case, it would not make sense to say that I should be writing a letter when my uncle entered the house, because I was actually writing a letter.