Here's a technique to achieve this.

$ perl -Mstrict -Mwarnings -E '
    my (%x, %y) = (a => 1, b => 2, c => 3, d => 1, e => 2, f => 1);
    push @{$y{$x{$_}}}, $_ for keys %x;
    say "$_: ", join ", ", @{$y{$_}} for keys %y;
'
1: a, d, f
2: b, e
3: c
[download]

I'll leave you to format the output however you want it.

Take note of the following excerpt from the keys documentation:

"The keys of a hash are returned in an apparently random order."

The output shown above was not modified to appear sorted! Here's two more runs also with unmodified output:

$ perl -Mstrict -Mwarnings -E '
    my (%x, %y) = (a => 1, b => 2, c => 3, d => 1, e => 2, f => 1);
    push @{$y{$x{$_}}}, $_ for keys %x;
    say "$_: ", join ", ", @{$y{$_}} for keys %y;
'
2: e, b
1: d, a, f
3: c
[download]

$ perl -Mstrict -Mwarnings -E '
    my (%x, %y) = (a => 1, b => 2, c => 3, d => 1, e => 2, f => 1);
    push @{$y{$x{$_}}}, $_ for keys %x;
    say "$_: ", join ", ", @{$y{$_}} for keys %y;
'
3: c
1: f, d, a
2: b, e
[download]

Update: As ++LanX points out (below), this may not be the clearest example. Here's, hopefully, a better one. This doesn't change the logic, just the clarity.

$ perl -Mstrict -Mwarnings -E '
    my %orig = (a => 1, b => 2, c => 3, d => 1, e => 2, f => 1);
    my %temp;
    push @{$temp{$orig{$_}}}, $_ for keys %orig;
    say "$_: ", join ", ", @{$temp{$_}} for keys %temp;
'
1: a, d, f
3: c
2: b, e
[download]