1. **Problem statement:** We are given 6 consecutive odd numbers whose sum is 204. We need to find the fourth number in this sequence. 2. **Formula and approach:** Let the first odd number be $x$. Since the numbers are consecutive odd numbers, the sequence can be written as: $$x, x+2, x+4, x+6, x+8, x+10$$ The sum of these 6 numbers is given by: $$x + (x+2) + (x+4) + (x+6) + (x+8) + (x+10) = 204$$ 3. **Simplify the sum:** $$6x + (2 + 4 + 6 + 8 + 10) = 204$$ Calculate the sum inside the parentheses: $$2 + 4 + 6 + 8 + 10 = 30$$ So, $$6x + 30 = 204$$ 4. **Solve for $x$:** $$6x = 204 - 30$$ $$6x = 174$$ $$x = \frac{174}{6} = 29$$ 5. **Find the fourth number:** The fourth number is: $$x + 6 = 29 + 6 = 35$$ **Final answer:** The fourth number in the sequence is **35**.