Parse error: syntax error, unexpected ‘}’ on get_the_author_meta [closed]

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Let’s unwrap it to more readable form:

<?php
    if ( ! empty( get_the_author_meta( 'facebook', $part_cur_auth_obj->ID ) ) ) {
?><a href="https://wordpress.stackexchange.com/questions/305172/<?php echo get_the_author_meta("facebook', $part_cur_auth_obj->ID);?>">
    <i class="fab fa-facebook-f"></i>
</a><?php}?>

End the last line is a problem. There are no spaces around curly bracket and it causes the error. Just change it to <?php } ?> and it will work fine.

So the rule is that you should put a space after <?php tag – it will cause problems otherwise. You can read more on this topic here: http://php.net/manual/en/language.basic-syntax.phptags.php

PS. If you combine PHP and HTML, it is better to use : notation for blocks and not brackets, I guess. It’s easier to keep track with all those endifs, endwhiles and so on than with a lot of }.