What this error message means is that the parameter for mysql_fetch_array() ($hasil in this case) is a boolean (hence "boolean given") rather than a MySQL resource. This means that [man]mysql_query/man must have returned FALSE, which it will do when your SQL query has an error.
The way I normally debug SQL errors quickly would be to alter your code like so:
$tampil="SELECT * FROM belajar LIMIT $posisi,$batas";
$hasil=mysql_query($tampil) or die("SQL error: " . mysql_error() . "<br><br>Query: $tampil");
Change your code such that it looks like what I have above and let us know what the MySQL error message is as well as what your query looks like.