<?php

$a = '<div style="text-align:center;"><!--image_begin:https://dl.site.com/20/NTQ3Nw==/Fists.jpg|--></div>';

preg_match('/dle_image_begin:(.+)|-->/', $a, $b);

print_r($b);

Array
(
    [0] => image_begin:https://dl.site.com/20/NTQ3Nw==/Fists.jpg|-->
    [1] => https://dl.site.com/20/NTQ3Nw==/Fists.jpg
)