SQL IN doesn't work to filter table
You need to join the mentors to the students, which translates here to a self join of students and then join the districts twice, once for the students and once for the mentors. Then you can filter by the countries.
SELECT ss.student_id
       FROM students ss
            INNER JOIN students sm
                       ON sm.student_id = ss.mentor
            INNER JOIN districs ds
                       ON ds.district_id = ss.district_id
            INNER JOIN districts dm
                       ON dm.district_id = sm.district_id
       WHERE ds.name = '&lt;the country the students should be from&gt;'
             AND dm.name = '&lt;the country the mentors should be from&gt;';

Some notes:

It is recommended to use modern, explicit JOIN syntax over old style joins with a comma separated list in the FROM clause. The former are easier to write without errors, to read and understand and maintain.
Do not use double quotes for string literals. In SQL string literals are quoted using single quotes. MySQL does accept double quotes but your code will be more portable when you use single quotes. And you'll get used to it and aren't in for surprises should you write a query for another DBMS.
In this case the question was easy enough to understand without it. But next time make sure to include sample input, i.e. sample data for the tables you work with, preferably as INSERT statements. Your current result as well as the desired result is absolutely meaningless without it. Of course you should also include your desired result. But never omit sample data, if you want to help those who try to help you.