Emir-says Keyarn Read this Tutorial well and follow each procedures carefully..
How to Display Featured Image On Carrington Mobile Theme Homepage
First Install Auto Post Thumbnail Plugin and Activate the follow the steps below
Follow these 3 steps to display featured image on Carrington mobile theme homepage

Step 1: We need to add featured image support to Carrington theme, to do this Login to your WordPress Dashboard, Goto Appearance, Click on Editor, On the Editor page Choose Carrington and click on select. (the page reloads). Scroll down a bit,

Now click on theme functions, Copy and paste the following code on the last line before the closing ?> tag in theme functions (also known as functions.php)

add_theme_support('post-thumbnails'); set_post_thumbnail_size(40,40);

Step 2: We need to call the featured image for each post to be displayed on the homepage, to do this Login to your WordPress Dashboard, Goto Appearance, Click on Editor, On the Editor page Choose Carrington and click on select. (the page reloads). Now click on loop-default.php, within the codes look for cfct_excerpt(); and paste the following code above it and save changes. (This is responsible for displaying the featured image before each post title on the homepage if a featured image has been set.)

if(has_post_thumbnail()) { the_post_thumbnail();}

Step 3: We need to style the featured image for it to be displayed properly beside the post title on the homepage, to do this Login to your WordPress Dashboard, Goto Appearance, Click on Editor, On the Editor page Choose Carrington and click on select. (the page reloads). Now scroll down and click on style.css, Copy and paste the following code on the last line of Style.css.

img { height: auto; max-width: 99%; } .wp-post-image { float: left; margin: 0 11px 0 0; padding: 2px 0 5px !important; } ul.table.disclosure li, ul.table li.disclosure { clear: both; margin: 0; padding: 0 0 0 3px !important; position: relative; }

Note: There is manual way of adding featured image on mobile themes which can also be done without any plugin but the codes will have to be designed in the Theme (That is kinda hard for Newbie).
I recommend this plugin type because it is automatic and easy to achieve. The function of plugin is that it will Auto Get first image of your post and set as the featured image..
As soon as you edited the theme with the above codes i dropped for you {make sure you followed the steps carefully because any mistake will crash the Theme}.
Reply if you still have any questions.