How to Highlight current category on category and single page template?

You can do something like

    <?php
        $current_category = get_the_category();
        /* 
           $current_category[0]->ID is holding the current category now. 
           If there are more than 1 categories for the post you should iterate
           through all of them and check if the current category you're 
           displaying is in there
        */

        $cats = get_categories('hide_empty=0&child_of=2&orderby=count&number=99&order=asc');
        foreach ((array)$cats as $cat) {
            $catdesc = $cat->category_description;
            ?>
            <li class="<?php echo ( ( $current_category[0]->ID === $cat->ID )? 'current' : '' ); ?>">
                <a href="https://wordpress.stackexchange.com/questions/131081/<?php echo get_category_link($cat); ?>" title="<?php echo strip_tags($catdesc); ?>">
                    <img src="<?php echo get_home_url (); ?>/wp-content/uploads/<?php echo $cat->slug ?>" alt="<?php echo $cat->cat_name; ?>" class="front-img">
                </a>
            </li>
        <?php } ?>