How to compute for Distance Modulus' uncertainty/ies?
You can just use these upper and lower bounds to create an upper/lower bound for the distance modulus. The lower bound is $168-14.9 = 153.1$, and the upper bound is $168+27.5 = 195.5.$ You can calculate the distance moduli for these values to get upper and lower bounds:
$$5\log(153.1) - 5 = 5.924876 \\ 5\log(195.5) - 5 = 6.455734$$
Then we calculate the distance modulus of the base value: $$5\log(168) - 5 = 6.126546$$
To get the deviations, we just subtract the distance moduli from the original. Therefore, your distance modulus is equal to $6.126546_{- 0.20167}^{+0.329188} \text{ pc.}$ I hope this helps. If there are any issues with my answer, please notify me.