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This puzzle can be solved directly using the [[

`SubstitutedExpression()`

]] solver from theenigma.pylibrary.The expressions can be specified on the command line, or as the following run file. Execution time is 130ms.

Run:[ @repl.it ]Solution:TWELVE = 160380.The full sum is: 972 × 165 = 160380.

By itself, the alphametic multiplication SIX × TWO = TWELVE has three solutions:

The first of these is the only solution where TWO is a multiple of 2.

The second of these is the only solution where SIX is a multiple of 6, and also where TWELVE is a multiple of 12.