Hoy, lisette a la bibioteca para estudiar.

I think the answer would be va because it is talking about a person and va is the el, ella, ud conjugation for ir which means "to go" so the answer in english would be Today Lisette goes to the library to study

The answer to your question is va because va is a form of ir which means to go. When translated with va in the blank, it means today, Lissette goes to the library to study. Any other verb like querer or gustar wouldn't work because if u add querer in there, it would be Hoy, Lisette quiere a la bibioteca para estudiar whcih wouldnt make sense. Same with gustar so va is your only choice.

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Mi familia y yo siempre íbamos juntos a salas de juegos y frecuentamos los fines de semana. nuestros pasatiempos solían ser jugar juegos de mesa y visitar a nuestros otros amigos y familiares.