僕がこの質問に答えるのは不可能だった。

。

It was impossible for me to answer this question.

Literal

I [subject-が] this question [to-に] answer [nominalizer-の] [topic-は] impossible was.

Cleft focus structure: [僕がこの質問に答える] nominalized as のは = 'my answering this question.' 不可能 ('impossible') is a formal na-adjective. Note the negating prefix 不 attached to 可能 ('possible') — a productive negative morpheme in Japanese.