So, the map is from the Event Manager plugin (https://elgg.org/plugins/736695). Best would be to ask the developers (from Coldtrick) directly how to do it or to suggest it as as a feature request. The same developers also offer the Widget Manager plugin (https://elgg.org/plugins/384604) that allow to built an home page / index page quite easily. Maybe they could add an index page widget to the Event Manager plugin that can be added to the index page provided by the Widget Manager plugin. But the best way to proceed is probably to ask the guys from Coldtrick directly.

@Bereng

I assume you're using Elgg 4.

I also assume that you've activated Front Page Demo plugin.
If so, here's what you can do.

Create 'custom_index\events_map.php' file in your custom plugin.

(You can use the skeleton My plugin if you haven't own plugin.)

So your new file should be located at:

\mod\my_plugin\views\default\custom_index\events_map.php

With this code:

<?php


$maps_provider = elgg_get_plugin_setting('maps_provider', 'event_manager');


if (elgg_is_active_plugin('event_manager') && $maps_provider !== 'none') {

      echo elgg_view_module('featured', elgg_echo('event_manager:list:upcoming'), elgg_view('event_manager/listing/map'));

}

Extend 'index/righthandside' view (or 'index/lefthandside' if you want to see your events module on the left side on the main page) with this new view in your elgg-plugin.php:

'view_extensions' => [

    'index/righthandside' => [
         'custom_index/events_map' => [],
    ]

],

Elgg docs.