"without a singl loop"

Direct hash lookups indeed work without loops.

So how can i correct my mistake ?

which mistake? Got some error? Some code, apart from that multilevel hash lookup?

From what you say I figure you mean

my $x = $hash{$valueM}{$key};
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because you say "where the mainKey equals $valueM". As you have written that multilevel hash lookup, the string contained in $valueM would be one key in an anonymous hash stored as the value for the key 'mainKey' in the hash %hash. I guess that's different to what you wrote. But how can I know? I know what I mean. Why don't you?

_($_=" "x(1<<5)."?\n".q·/)Oo.  G°\        /
                              /\_¯/(q    /
----------------------------  \__(m.====·.(_("always off the crowd"))."·
");sub _{s./.($e="'Itrs `mnsgdq Gdbj O`qkdq")=~y/"-y/#-z/;$e.e && print}

   $x = $hash{$valuem};
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"without a singl loop"

use strict;
use warnings;
my $valueM = 'myvalue';
my $hashref;
$$hashref{mainKey}{$valueM}{key} = 'value';
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my %hash;
$hash{key} = 'value';
...
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