The two ways of relating what a person has said are 1)direct and 2)indirect (reported speech).In direct speech, the original speaker's exact words are repeated. Direct speech is found in plays and quotations. In indirect/reported speech, the exact meaning is expressed but not necessarily using the original speaker's exact words. Pronouns and possessive adjectives usually change from first or second person to the third person except when the speaker is reporting his own words. Sometimes a noun can be inserted to avoid doubt.
Options B and C are correct as the given question is transformed to the assertive form, simple present tense is changed to simple past tense, and if/whether is used as the given question doesn't start with a question word.
Options A and D are wrong as 'that' cannot be used in the transformation and 'was' is missing respectively.
The correct answers are B)He asked me if I was glad to be back. and C) He asked me whether I was glad to be back.