The correct answer is D. Writing a former teacher to ask for a letter of recommendation
Step-by-step explanation:
Formal language in English refers to a style in writing and speaking in which you follow in a strict way grammar and styles rules; avoid the use of contractions, slangs or words that are informal and colloquial; use third person rather than the first person and in general terms use language in a polite and serious way. Additionally, formal language is linked to showing respect to others and giving a good impression of yourself. Some of the contexts in which you should use formal language are in academical or professional contexts, in any written or oral communication such as letters or emails with your superiors such as your boss or teachers and in situations where you communicate with people you do not know well.
Considering this, the case or situation in which it would be more appropriate to use formal language rather than informal language is "writing a former teacher to ask for a letter of recommendation" as this is a formal context in which you are speaking to some superior or authority figure; also as you are asking for a favor it is quite important to show that you care about the use of language and give a good impression to your teacher, which is not required in the other situations presented.