To solve this equation, we need to first convert the mixed numbers into improper fractions.

X - 49 7/12 = 51 5/6 + 10 1/18

Convert 49 7/12 into an improper fraction:

49 + 7/12 = (49 * 12 + 7) / 12
49 + 7/12 = 595 / 12

Convert 51 5/6 into an improper fraction:

51 + 5/6 = (51 * 6 + 5) / 6
51 + 5/6 = 311 / 6

Convert 10 1/18 into an improper fraction:

10 + 1/18 = (10 * 18 + 1) / 18
10 + 1/18 = 181 / 18

Now our equation becomes:

X - 595/12 = 311/6 + 181/18

Next, find a common denominator for all the fractions, which in this case is 36:

X - (595 3) / (12 3) = (311 6) / (6 6) + 181/18
X - 1785 / 36 = 1866 / 36 + 181 / 36

Now combine the fractions:

X - 1785 / 36 = 2047 / 36

Add 1785 to both sides:

X = 2047 / 36 + 1785 / 36
X = 3832 / 36
X = 106 10/36
X = 106 5/18

Therefore, the solution to the equation is:

X = 106 5/18