趣味 and 娯楽: personal hobbies and entertainment

Distinguish a personal interest from the broader range of entertainment.

A personal hobby

趣味 (しゅみ) means hobby. 「趣味は写真を撮ることです」 identifies taking photographs as the speaker's hobby.

「趣味で絵を描いています」 says the speaker paints or draws as a hobby. It does not establish a professional artist's occupation.

娯楽 (ごらく) means entertainment or recreation. 「旅行先で娯楽を楽しみました」 describes enjoying entertainment while traveling.

「娯楽のために使う時間を減らしました」 says time spent on entertainment was reduced. It does not mean stopping all enjoyment.

A hobby may also be 娯楽, so the categories overlap. 趣味 focuses on personal interests, while 娯楽 focuses on enjoyable activities or offerings.

「私の趣味には合いません」 can mean something does not suit the speaker's taste. 趣味 is not always a repeated leisure activity.

Show the answer and why

No. It describes a hobby; occupation is separate.