Why doesn't 'amenerai' work?
I believe because the sentence uses "going to" so we gotta translate it using «aller» instead of the future tense.
The hints show "à" first for "by" car, but the answer requires "en"?
A vélo, à pieds, en voiture, en train... You need to learn this.
If it's a vehicle that you get into like a car, bus, train, or plane then we use «en» .