The third digit of four digits is 6, and the number divisible by 3 is (999-99)/3=300.

The second digit of four digits is 6, and the number divisible by 3 is (999-99)/3=300.

The first digit of a four-digit number is 6, and the one divisible by 3 is [1000/3] = 33 1.

The third digit of the four-digit number is 6, and the fourth digit is also 6. 300/ 10=30 is divisible by 3.

The second digit of the four-digit number is 6, the third digit is 6, and the fourth digit is 6. Divisible by 3 is (300/ 10)/ 10=3.

The first digit of the four digits is 6, the second digit is 6, the third digit is 6, and the fourth digit is 6. Divisible by 3 is 1.

300+300+300+33 1-30-3- 1= 1 197

Answer: The four-digit number including the number 6 and divisible by 3 is 1 197.