You would have to navigate to the /wp-content/themes/”your theme name”/ and while each theme differs, it should be somewhere in there, not necessarily in index.php. You may need to edit loop.php, or single.php depending.
Other than that, you could hide this by editing your style.css file.
Below Line 963, add display: none to the .entry-meta block of CSS.
NOTE: This will hide anything across the website that is displayed in the entry-meta div.