A few things:

1. Check out perldoc perlsub for information about using prototypes and what &j() actually does.
2. sub j ($i,$j,$k) { should be replaced with sub j { ($i,$j,$k) = @_;
3. To get a reference to a sub, use \&h.

Put it all together and you get:

sub h {
    my ($x,$y)=@_;
    print "the val of x is $#$x and y is $#$y\n";
}
sub j {
    my ($i, $j, $k) = @_;
    print "\ni am in the function j\n\n";
    &$k($i,$j); # or $k->($i,$j);
}
my @ar = qw/1 2 3 4/;
my @vr = qw/56 7 8 9/;

j(\@ar, \@vr, \&h);
__END__
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You need to include the & when you take the reference (otherwise your calling h and then taking a reference to teh result):

j (\@ar, \@vr, \&h);
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And for most ordinary uses you can drop the & when calling the function as above. To invoke the coderef I prefer to use ->:

$k->($i,$j);
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$#$x will print the last subscript value of the refered array. To find number of contents $#$x has to be $#$x + 1.

Now the subroutine h will be called inside the subroutine j.

sub h {
    my ($x,$y)=@_;
    print "the val of x is $#$x and y is $#$y\n";
}
sub j {
    my ($i, $j, $k)=@_;
    print "\ni am in the function j\n\n";
    &$k($i,$j);
}
@ar = qw/1 2 3 4/;
@vr = qw/56 7 8 9/;

&j (\@ar, \@vr, \&h);
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You seem to know some programming but try to brute-force Perl, which doesn't work well with Perl.

For a quick introduction to Perl, read "perlintro" at www.perldoc.com.

Futher reading that may help you get started is "perl", "perltoc", "perldata", "perlsub", and "perlref" (also found at www.perldoc.com).

Other than that, you might want to read a tutorial or two. Just be aware of that there are many IMHO bad tutorial that teaches bad practices.

ihb

Read argumentation in its context!