B. I wanted to go to the beach, but my parents wouldn't let me.
C. She studied hard for the exam, however, she still failed.
D. I went to the store, bought milk, but forgot to buy eggs
Explanation
Incorrect use of conjunctive verbs: She studied hard for the exam, however, she still failed.
Explanation: "However" is a conjunctive adverb, not a coordinating conjunction. It needs proper punctuation (a semicolon or period before it). Correct: She studied hard for the exam; however, she still failed.