How to get a custom type post data when it has a connection with another custom type post?

If in a country looking for cities

$args = array (
    'post_type' => 'cities',
    'meta_key' => 'country',
    'meta_value' => get_the_ID()
);

This assumes that the “Country > Name* > [drop down]” you screenshot saves that the selected value using post_meta and is saving the country’s post ID. (If it does not please adjust or specify).

UPDATE

To list cities, and retrieve their country_name, assuming the dropdown is just storing the post_title of the country, you could do:

$cities = get_posts(array (
    'post_type' => 'cities',
    'numberposts' => '-1',
));
foreach ($cities as $city) {
    $country_name = get_post_meta($city->ID,'country_name',true);
    // to get the full country, if country_name is just the post title (and not ID) you could do
    # $country = get_page_by_title( $country_name, 'object', 'country' );
    echo "<pre>City: {$city->post_title} is in country: {$country_name}</pre>":
}