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.
