Hi,
To achieve that, add the code below in Theme Options > CSS
.x-post-carousel-meta>span.entry-cover-author,
.x-post-carousel-meta>span.entry-cover-date {
display:none;
}

Then create file _index-featured.php in x-child/framework/views/ethos/ and add the code below into that file.
<?php
// =============================================================================
// VIEWS/ETHOS/_INDEX-FEATURED.PHP
// -----------------------------------------------------------------------------
// Featured content output for the index pages.
// =============================================================================
$index_layout = get_post_meta( get_the_ID(), '_x_ethos_index_featured_post_layout', true );
$class = ( $index_layout == 'on' ) ? 'featured' : '';
$background_image_style = x_ethos_entry_cover_background_image_style();
$categories = x_ethos_post_categories();
?>
<a href="<?php the_permalink(); ?>" class="entry-thumb <?php echo $class; ?>" style="<?php echo $background_image_style; ?>">
<?php if ( $index_layout == 'on' && ! is_single() ) : ?>
<span class="featured-meta"><?php echo $categories; ?> </span>
<h2 class="h-featured"><span><?php the_title(); ?></span></h2>
<span class="featured-view"><?php _e( 'View Post', '__x__' ); ?></span>
<?php else : ?>
<span class="view"><?php _e( 'View Post', '__x__' ); ?></span>
<?php endif; ?>
</a>
You may refer to the video below for your guide on how to create file and folder using file manager
Hope that helps