How to test if a value exist in a hash?

Shorter answer using smart match (Perl version 5.10 or later):

print 2 ~~ [values %x];

Fundamentally, a hash is a data structure optimized for solving the converse question, knowing whether the key 2 is present. But it's hard to judge without knowing, so let's assume that won't change.

Possibilities presented here will depend on:

• how often you need to do it
• how dynamic the hash is

One-time op

• grep $_==2, values %x (also spelled grep {$_==1} values %x) will return a list of as many 2s as are present in the hash, or, in scalar context, the number of matches. Evaluated as a boolean in a condition, it yields just what you want.
  grep works on versions of Perl as old as I can remember.
• use List::Util qw(first); first {$_==2} values %x returns only the first match, undef if none. That makes it faster, as it will short-circuit (stop examining elements) as soon as it succeeds. This isn't a problem for 2, but take care that the returned element doesn't necessarily evaluate to boolean true. Use defined in those cases.
  List::Util is a part of the Perl core since 5.8.
• use List::MoreUtils qw(any); any {$_==2} values %x returns exactly the information you requested as a boolean, and exhibits the short-circuiting behavior.
  List::MoreUtils is available from CPAN.
• 2 ~~ [values %x] returns exactly the information you requested as a boolean, and exhibits the short-circuiting behavior.
  Smart matching is available in Perl since 5.10.

Repeated op, static hash

Construct a hash that maps values to keys, and use that one as a natural hash to test key existence.

my %r = reverse %x;
if ( exists $r{2} ) { ... }

Repeated op, dynamic hash

Use a reverse lookup as above. You'll need to keep it up to date, which is left as an exercise to the reader/editor. (hint: value collisions are tricky)

my %reverse = reverse %x;
if( defined( $reverse{2} ) ) {
  print "2 is a value in the hash!\n";
}

If you want to find out the keys for which the value is 2:

foreach my $key ( keys %x ) {
  print "2 is the value for $key\n" if $x{$key} == 2;
}