need a number
less than 1010
more than 960
divisible by 6
sum of digits is less than 5

Since the sum of the digits in the number must be less than 5, that rules out 960 through 999, because with that 9 in there, you've already exceeded that '5' sum requirement even without adding in any of the 2 other digits (for example, the sum of the digits in the number 961 is 9+6+1 = 16, which is more than 5, etc.).
So that leaves 1000 through 1010 to investigate, or the numbers
1000,1001,1002,1003,1004,1005,
1006,1007,1008,1009, and 1010.
Now you can rule out
1004,1005,1006,1007,1008, and 1009,
since the digits in those numbers add up to 5 or more.
So we're left with 1000, 1001, 1002, 1003, and 1010, all of which have a digit sum total of less than 5. But the number must also be divisible by 6, and by doing out the math, only 1002 is divisible by 6 (1002/6= 167 exactly).

Thanks, Les, for making ANSWERPOOL your Homework Help web page!