To solve this equation, we need to find the value of X that satisfies the equation:

X + 3/9 + X + 4/8 + X + 5/7 + X + 6/6 = -4

First, let's simplify the equation by finding a common denominator for the fractions:

X + 1/3 + X + 1/2 + X + 5/7 + X + 1 = -4

Now, let's combine like terms:

4X + 1/3 + 1/2 + 5/7 + 1 = -4

To add the fractions, we need to find a common denominator. The least common multiple of 3, 2, and 7 is 42:

4X + 14/42 + 21/42 + 30/42 + 42/42 = -4

Now, let's add the fractions:

4X + 107/42 = -4

To isolate X, we need to get rid of the fraction. We can do this by multiplying both sides of the equation by 42:

42(4X + 107/42) = -4(42)

Simplifying:

168X + 107 = -168

Now, let's isolate X by subtracting 107 from both sides:

168X = -168 - 107

168X = -275

Finally, divide both sides by 168 to solve for X:

X = -275/168

Therefore, the solution to the equation is X = -275/168.