Final answer:
The sentence should use 'that' to connect the clause 'had been missing for weeks' with the 'pencil case', making the sentence 'My pencil case, that had been missing for weeks, finally turned up yesterday'.
Step-by-step explanation:
The sentence 'My pencil case, had been missing for weeks, finally turned up yesterday' has a relative clause which provides additional information about the noun (pencil case). In this case, the appropriate pronoun to use is 'b. That' making the proper sentence: 'My pencil case, that had been missing for weeks, finally turned up yesterday'. The reason we use 'that' instead of 'which' is because the relative clause is essential to the meaning of the sentence. Without it, 'My pencil case finally turned up yesterday' may not make sense as it does not convey why the pencil case turning up is significant (it had been missing for weeks).
Learn more about Pronoun Usage