my %hash = (
    first  => { a => 2, b => 3 },
    second => { a => 3, b => 2 },
    third  => { a => 5, b => 4 },
    fourth => { a => 4, b => 6 },
);

my %newhash = map  { $_ => $hash{$_} }
              grep {     foo($hash{$_})
                     and bar($hash{$_}) }
              keys %hash;

print "$_\n" foreach keys %newhash;

sub foo {
    my ($href) = @_;
    $href->{a} > 3;
}

sub bar {
    my ($href) = @_;
    $href->{b} > 2;
}