Suman writes the number 8,1_4.
She wants it divisible by 6 (that is, by both 2 and 3).
How many digit values can fill the blank?

The last digit 4 is even, so the test for 2 always passes. For 3, the digit sum = 8 + 1 + blank + 4 = 13 + blank must be a multiple of 3. Trying blank = 0..9: 13+2 = 15, 13+5 = 18, 13+8 = 21 are multiples of 3. So blank can be 2, 5 or 8 — that is 3 values.