On line 2 you're not using open correctly, and not checking the return value for success (see perlopentut). You never read from a file at all. The rest accomplishes nothing useful.

Almost everything you need to accomplish this task is addressed in perlintro. Here is a solution expressed as a one-liner (which would also require reading a little from perlrun and perlrequick):

perl -nE '$count{$1}++ while /\b(the|hi|linux)\b/ig; END{say "$_ => $c
+ount{$_}" for keys %count}' filename.txt
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As a full script, it might look like this:

#!/usr/bin/perl

open $fh, '<', $ARGV[0] or die $!;

while( <$fh> ) {
  $count{$1}++ while /\b(the|hi|linux)\b/ig;
}

print "$_ => $count{$_}\n" for keys %count;
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Run it as:

Update: It would have been polite to let us know you are following up to the question you asked here: Help with accepting inputs, wordcount, and print to a file, if for no other reason than to provide us with that additional context.