Querying posts from wordpress with 2 or more conditionals

You can pass array with multiple queries to meta_query.

Something like:

'meta_query' => array(
        array(
            'key'     => 'eg-enddate',
            'value'   => date("d/m/Y"),
            'compare' => '>',
            'type'    => 'numeric'
        ),
        'relation' => 'AND',
        array(
            'key'     => 'eg-startdate',
            'value'   => date("d/m/Y"),
            'compare' => '<',
            'type'    => 'numeric'
        )
    )

For more please go through documentation: https://codex.wordpress.org/Class_Reference/WP_Meta_Query

Note: Code is not tried or tested so look out for syntax errors.