Well, you have 72 ways of choosing the first number, and for each of these you have 71 ways of choosing the second (so 72*71*70 and so far), and for each of those pairs you can pick the third number in 70 ways, etc.
So the number of ways of picking an *ordered* sequence of numbers in the desired range is 72 x 71 x 70 x 69 x 68 x 67.
But we only care about unordered sets of six numbers, not a sequence. We are over-counting: every combination of numbers will show up in our process exactly 6!=6x5x4x3x2x1=720 times, because this is just the number of ways to arrange six numbers in some order.
Therefore, the final answer is
72*71*70*69*68*67/(6*5*4*3*2*1)=156,238,908
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