Conditional Statement with Multiple Terms?

Firstly, create some sort of association between the icon class and the term name:

$icons = array(
    'webinar'          => 'fa-desktop',
    'report'           => 'fa-file-text-o',
    'video'            => 'fa-youtube-play',
    'past-project'     => 'fa-cogs',
    'meeting-material' => 'fa-users',
    'info-sheet'       => 'fa-info-circle',
);

Then loop through each term assigned to the post and output the corresponding icon:

$terms = get_the_terms( get_the_ID(), 'type' );

if ( $terms && ! is_wp_error( $terms ) ) {
    foreach ( $terms as $term ) {
        $class = isset( $icons[$term->slug] ) ? $icons[$term->slug] : 'fa-link';

        echo '<i class="fa ' . $class . '" aria-hidden="true"></i>';
    }
}