To solve this expression, we need to simplify each fraction individually and then perform the subtraction.

First, let's simplify each fraction:

-15/14 = -1 1/14
17/23 = 17/23
15/14 = 1 1/14
17/11 = 1 6/11
6/7 = 6/7

Now, let's substitute the simplified fractions back into the expression:

-1 1/14 : 17/23 - 1 1/14 : 1 6/11 - 6/7

Next, let's convert the mixed numbers into improper fractions:

-1 1/14 = -15/14
1 1/14 = 15/14
1 6/11 = 17/11

Now, we can rewrite the expression:

-15/14 : 17/23 - 15/14 : 17/11 - 6/7

Finally, let's perform the subtraction:

-15/14 : 17/23 = (-15/14) / (17/23) = (-15/14) * (23/17) = -345/238

-15/14 : 17/11 = (-15/14) / (17/11) = (-15/14) * (11/17) = -165/238

Now, we can rewrite the expression with the simplified fractions:

-345/238 - 165/238 - 6/7

To subtract fractions, we need a common denominator. In this case, the common denominator is 238:

-345/238 - 165/238 - 6/7 = (-345 - 165)/238 - 6/7 = -510/238 - 6/7

To subtract fractions, we need a common denominator. In this case, the common denominator is 238:

-510/238 - 6/7 = (-510 * 7)/(238 * 7) - (6 * 238)/(7 * 238) = -3570/1666 - 1428/1666

Now, we can subtract the fractions:

-3570/1666 - 1428/1666 = (-3570 - 1428)/1666 = -4998/1666

Finally, we can simplify the fraction:

-4998/1666 = -2499/833

Therefore, the simplified expression is -2499/833.