Please go to My Site → Customize → CSS (or Additional CSS), then add all of the following code to the bottom of that window.
/* This CSS hides the author byline on posts.
* 11445317-hc (jw)
*/
.byline,
.entry-meta ul>li:before {
display: none;
}
Tip: keep the /*
comment */
in the code to later know what this code does.