Agloria
zanahorias.
las
1. le encanta
a maría
comer el
queso y las zanahorias.
2. le encantan
las
a mí no
papas.
3. me gustan
4. me gusta
a mí comer las
papas y los frijoles.

we must complete the blanks with the given options:

1) A Gloria zanahorias.

Now, Gloria is in singular, and Zanahorias is in plural (words that end with an -s usually are plural), and we are talking of Gloria, so the person is "Ella", then the correct option here is "Le encantan", where the fact that "encantan" ends with an -n means that refers to something in plural.

A Gloria le encantan las zanahorias.

2) A Maria comer el queso y las zanahorias.

Now, again, Maria is in singular, the person is "ella", but now we are talking about a verb, "comer", so the correct option here is "Le encanta"

AMaria le encanta comer el queso y las zanahorias.

3) A mi no las papas.

Now, the person is "yo", and again, papas is in plural, so the correct option is "me gustann"

A mi no me gustan las papas.

4)  A mi comer las papas y los frijoles.

Again, the person here is "Yo", and now we are talking to a verb, so does not mater that "Papas y frijoles" are in plural, the correct option here is "Me gusta"

A mi me gusta comer las papas y los frijoles.