The goal of my query is to return the country name and its head of state if it\'s headofstate has a name starting with A, and the capital of the country has greater than 100
You need to join the two tables and then filter the result in where clause:
SELECT country.name as country, country.headofstate
from country
inner join city on city.id = country.capital
where city.population > 100000
and country.headofstate like 'A%'