To solve this equation, we need to simplify the expression on the left side:

X - (-4,6 + 3 4/7) = -8 1/14

First, we need to add the mixed number 4,6 and the fraction 3 4/7 together:

4 6 + 3 4/7 = 4 + 3 + 6 + 4/7 = 7 + 10/7 = 7 3/7.

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

X - 7 3/7 = -8 1/14

To solve for X, we can add 7 3/7 to both sides of the equation:

X - 7 3/7 + 7 3/7 = -8 1/14 + 7 3/7

X = -8 1/14 + 7 3/7

Now, we need to find a common denominator to add the fractions on the right side. The common denominator for 14 and 7 is 14:

X = -82/14 + 72/7
X = -16/14 + 14/14
X = -2/14

Finally, we can simplify the fraction:

X = -1/7

Therefore, the solution to the equation X - (-4,6 + 3 4/7) = -8 1/14 is X = -1/7.