Certain DS questions become easier to deal with if you 'rewrite' the question (as Bunuel showed in his explanation). For this prompt, you do not have to do that work to get the correct answer, but you will have to do some basic math regardless of how you approach the prompt.
Here, we're asked if the average of 6 terms (C, 8C, 2C, 5C, 4C and 4C) is greater than 8. This is a YES/NO question. Since the two Facts give us inequalities to work with, we can use each of them (individually) to figure out whether the average has a maximum or minimum possibility.
Fact 1: C < 4
We can use C = 4 as our "upper boundary"; in this case, the average of the 6 terms would be...
(4+32+8+20+16+16)/6 = 96/6 = 16
Since C is LESS than 4, the average of these 6 terms is LESS than 16.
IF....the average = 15, then the answer to the question is YES.
IF....the average = 0, then the answer to the question is NO.
Fact 1 is INSUFFICIENT
Fact 2: C > 2
Much as we did in Fact 1, we can use C = 2 as our "lower boundary"; in this case, the average of the 6 terms would be...
(2+16+4+10+8+8)/6 = 8
Since C is GREATER than 2, the average of these 6 terms is GREATER than 8.
Since the question asks if the average is greater than 8, the answer to the question is ALWAYS YES.
Fact 2 is SUFFICIENT.
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