Step 1: How a telescope length works.
For an astronomical telescope set in normal adjustment, the tube length equals the sum of the two focal lengths: \[ L = f_o + f_e. \]
Step 2: Read the given relation carefully.
The objective focal length is $850\%$ more than the eyepiece. Being $850\%$ more means we add $8.5$ times to the original, so $f_o = f_e + 8.5\,f_e = 9.5\,f_e$.
Step 3: Put this into the length equation.
\[ L = 9.5\,f_e + f_e = 10.5\,f_e. \]
Step 4: Solve for the eyepiece focal length.
The length is $126\,\text{cm}$, so \[ 126 = 10.5\,f_e \;\Rightarrow\; f_e = \frac{126}{10.5} = 12\ \text{cm}. \]
Step 5: Quick sanity check.
Then $f_o = 9.5 \times 12 = 114\,\text{cm}$, and $114 + 12 = 126\,\text{cm}$, which is exactly the tube length given. So the numbers fit.
Step 6: Conclusion.
The eyepiece focal length is $12\,\text{cm}$. \[ \boxed{12\ \text{cm}} \]