To solve the equation 4 1/12 - 15/6x = 2 17/24, we first need to convert all the mixed numbers to improper fractions for easier calculation.

4 1/12 = 49/12
2 17/24 = 65/24

Now, the equation becomes:
49/12 - 15/6x = 65/24

We need to find a common denominator for the fractions on both sides of the equation. The least common multiple of 12, 6, and 24 is 24.

Multiplying the first fraction by 2/2 and the second fraction by 4/4 to get a common denominator of 24, we get:
(492)/(122) - (154)/(64)x = 65/24
98/24 - 60/24x = 65/24

Now, we can combine the fractions:
38/24 - 60/24x = 65/24

Subtracting 38/24 from both sides, we get:
-60/24x = 27/24

Dividing by -60/24 to solve for x, we get:
x = (27/24) / (-60/24)
x = 27/24 * -24/60
x = -27/60
x = -9/20

Therefore, the solution to the equation 4 1/12 - 15/6x = 2 17/24 is x = -9/20.