Solution: Twin Letters

The code...

declare
% A B C  *  D E F
% _______________
%           G H I
%         J K L
%       M N O
% _______________
%       P Q R S T

proc {Twice Root}
   A B C D E F G H I J K L M N O P Q R S T
   C1 C2 C3
in
   Root = solution(a:A b:B c:C d:D e:E f:F g:G h:H i:I j:J
                   k:K l:L m:M n:N o:O p:P q:Q r:R s:S t:T)
   Root ::: 0#9
   C1 :: 0#1
   C2 :: 0#2
   C3 :: 0#1
   %CarriesLow ::: 0#9
   %CarriesHigh ::: 0#1
   
   {For 0 9 1
    proc {$ I} {FD.exactly 2 Root I} end
   }
                      100*G + 10*H + I +
             1000*J + 100*K + 10*L +
   10000*M + 1000*N + 100*O =:
   10000*P + 1000*Q + 100*R + 10*S + T

   (100*D + 10*E + F)*C =: 100*G + 10*H + I
   (100*D + 10*E + F)*B =: 100*J + 10*K + L
   (100*D + 10*E + F)*A =: 100*M + 10*N + O
   
   (100*A + 10*B + C) * (100*D + 10*E + F) =:
   10000*P + 1000*Q + 100*R + 10*S + T
   % Carry restrictions
   T         =: I
   S + 10*C1 =: H + L
   R + 10*C2 =: G + K + O + C1
   Q + 10*C3 =: J + N + C2
   P         =: M + C3
   
   {FD.distribute generic(order:size) Root}
end

{ExploreOne Twice}

...and the search tree

The only solution then is

Q=R=0, D=H=1, A=B=2, J=M=3, C=P=4, 
K=N=5, I=T=6, E=G=7, L=O=8, F=S=9

224 * 179
_________
      716
     358
    358
_________
    40096