Final answer:
The correct preposition to complete the sentence is "por" because it indicates the means by which someone is going to call their mother.
Step-by-step explanation:
The correct preposition to complete the sentence is por. The sentence should be "Necesito comunicarme con mi mamá; es muy importante. Voy a llamarla por teléfono." In this context, "por" is used to indicate the means by which someone is going to call their mother, which is through the telephone.
Learn more about Prepositions in Spanish