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This is "mod n" language..and the idea behind construction of DFA for "mod n" language is that Make States corresponding to each possible remainder of $n$ and then make transitions accordingly. Such machines are simplest to construct.

The DFA for the given language will look like the following :

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I couldn't draw the diagram properly thats why i am giving one of the image drawn in book.

Here the states 00, 02, 10, 11, 21, 22 will be the final states as the condition is sum of (n+ 2nb) mod 3 < 2

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