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.

But have you written the language yet? If so, what's it called and where can we read about it?

To progress with Perl, you really need to read a primary text ("Learning Perl" leaps to mind) because, as a wise person once said, 'You can't just make stuff up and expect the computer to understand.'

And, as various Monks have observed, it's well to acknowledge the fact when you're asking for help with homework.