In order to answer a few difficult questions, I had to run to two different departments to obtain the answers.
ご質問ありがとうございます。
"In order to answer a few difficult questions,"=「複雑な質問をいくつか答えるために」
"I had to run to two different departments to obtain the answers."=「私は二つ違う部署に走って回答を得なければいけなかった。」
☆「複数」が2,3問の場合は"a few"になりますが、それ以上でしたら"many"を使うことが良いと思います。
ご参考に。