Right answer: debe
In Spanish (castilian), the verb deber (to owe) means to have a debt to someone.
However, the verb debe have another meaning:
must
This acts as an auxiliary verb (similar to English), being written before the main verb of the sentence. This use of the verb debe is called verbal periphrasis or verbal phrase, and generally is written in a sentence as follows:
Subject + debe (must) + main verb in infinitive + complement
And, for this case the meanings are as follows:
a) deber: implies obligation or need, but can also express assumption or belief (the first option is preferred).
Example: Ana debe estar en la escuela
Ana must be at school
This may mean:
1. It is mandatory that Ana is in school
2. I guess Ana is in school
b) Deber de: only expresses assumption or belief.
Example: Ana debe de estar en la escuela
Ana must be at school
It means that:
I guess Ana is in school
Now, in the following sentence, the main verb fumar (to smoke) is in the infinitive and with the 3rd person in singular la gente (the people). From there it follows that the auxiliary verb debe must be used.
Then the complete sentence is:
En los restaurantes de Ecuador, la gente debe fumar en el exterior.
In restaurants in Ecuador, people must smoke outside.
Indicating that it is an obligation that people smoke outside.
The other options are incorrect because they do not fit in the context of the sentence:
Necesario means necessary
ni means neither
siempre means always