The number 5_4 is divisible by 6. What is the missing tens digit (smallest possible)?

Divisible by 6 means divisible by 2 and 3. The last digit 4 is even, so the 2-test passes. Digit sum = 5 + blank + 4 = 9 + blank must be a multiple of 3, so blank is a multiple of 3. The smallest digit is 0 $(504=6\times 84)$.