This is the 660th most frequent Japanese word.
飲み
"飲み" (nomi) means "drinking."
In this instance, '飲み' (nomi) is used as part of the verb '飲みたくない' (nomitakunai), expressing a desire not to drink or take medication in this context.
彼女は薬を飲みたくないと言いました。
She said she does not want to take the medicine.
Although '飲み' directly isn't in this sentence, the context of '晩酌' (banshaku) inherently involves the action of drinking. This reflects a cultural context where drinking is a social activity.
友達と一緒に晩酌を楽しみます。
I enjoy having a drink with friends in the evening.
Here, '飲み' (nomi) is part of the verb '飲みます' (nomimasu), which is the polite form for 'to drink'. It indicates the action of consuming a beverage.