I've my sites setup like so:

mywebsite/directory1/index.php
mywebsite/directory2/index.php
mywebsite/directory3/index.php
mywebsite/directory4/index.php

this isn't Search engine optimization friendly. How do i use mod_rewrite to complete the next:

mywebsite/directory1/
mywebsite/directory2/
mywebsite/directory3/

How do i make search engines like google crawl my website with no issues of getting multiple index.php´s?

What exactly are you professional suggestions?

Place this to your root .htaccess file:

RewriteEngine On
#if your index.php is located in the root folder:
RewriteBase /
#or use that, if the path for your index.php is '/some/subfolder/index.php':
#RewriteBase /some/subfolder/

#rewriting only if the request file doesn't exists (you don't want to rewrite request for images or other existing files)
RewriteCond %{REQUEST_FILENAME} !-f
RewriteRule ^(.*)? index.php?path=$1 [L]

Next, you should use the REQUEST_URI inside your root index.php file:

var_dump($_SERVER['REQUEST_URI']);

or use $_GET['path']:

var_dump($_GET['path']);

Inside your HTML and CSS, use absolute path for images along with other assets (or better use full URL's):

<img src="/image/image.jpg" alt="image" />