Answer: 1. me gusta 2. Te gustan 3. me gustan 4. le encantan
Explanation: We need to complete the conversation:
—Buenos días, Francisco, a mí 1. ________ mucho comer maíz y zanahorias. ¿2. ________ las zanahorias?
—Hola, no 3. ________ las zanahorias, pero a mi mamá Juana 4. ________ los tomates.
1) here we are talking about "mí" that is a way to talk about ourselves, then the right option, in this case, is "me gusta"
2) here we are talking to Francisco, and we want to ask him if he likes the carrots, so we are also talking in the plural, then the right option here is "te gustan"
3) Now Francisco is answering, so he is talking in the first person, then the right option is "me gustan".
4) Now Francisco is talking about his mother, so the right option here is "le encantan".
the complete sentence would be:
—Buenos días, Francisco, a mí me gusta mucho comer maíz y zanahorias. ¿Te gustan las zanahorias?
—Hola, no me gustan las zanahorias, pero a mi mamá Juana le encantan los tomates.