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esta noche _______ tengo que escribir una carta a carmen

I need to fill in the blank with one of these words: le les lo la los or las
I am not understanding this concept at all

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Ed M. | Help with grammar, French, SAT Writing, the TOEFL and ESL.Help with grammar, French, SAT Writing, ...
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I hope you understand the meaning of your Spanish sentence as it stands: 'Tonight I have to write a letter to Carmen'. That is, the Spanish sentence contains a transitive verb (in its infinitive form) escribir 'to write' which has both a direct object una carta 'a letter' and an indirect object a Carmen 'to Carmen'.
Spanish also has indirect object pronouns which unlike in English are often used even when the indirect object is stated explicitly. For example, in the English equivalent of your Spanish sentence, if I replaced the full indirect object to Carmen with just a pronoun, the sentence would be Tonight I have to write her a letter (or Tonight I have to write a letter to her). In Spanish, however, it is not uncommon for both an indirect object and an indirect object pronoun referring to it to occur in the same sentence, which in English would be redundant.
So among the selection of pronouns you give, only le and les are indirect object pronouns in Spanish, the former singular and the latter plural, and both of these can be either masculine or feminine, i.e., they can refer to an indirect object that's either masculine or feminine in grammatical or real gender. That indeed is sometimes a source of ambiguity in Spanish, e.g., Le escribo la carta could mean 'I write him the letter',  'I write her the letter' or even 'I write you-FORMAL-SINGULAR (i.e., usted) the letter'. As a result, again unlike in English even if an indirect object pronoun is included, often the full indirect object is still stated for clarity.
So in your Spanish sentence, I believe the correct pronoun to choose is le, which would refer to the indirect object a Carmen containing the name of a single person (presumably, as in most Spanish-speaking countries, a female, but fortunately the facts of Spanish grammar would constrain you to use le anyway even if Carmen were male).