What happens when mixing elemental mercury with sodium hypochlorite solution
There are several redox reactions can be taken place when you add household beach on elemental mercury metal. However, this question is more like a homework question. Thus, I give you insight to the answer and you may read a bit and find out what's happening. This reaction is studies and results have been published (Reference 1), the abstract of which states that:


  The absorption of elemental $\ce{Hg}$ vapor into aqueous hypochlorite was measured in a stirred tank reactor at $25$ and $\pu{55 ^{\circ}C}$. $\ce{NaOCl}$ strongly absorbs $\ce{Hg}$ even at high pH. Low $\mathrm{pH}$, high $\ce{Cl-}$ and high-temperature favor mercury absorption.  Aqueous free $\ce{Cl2}$ was the active species that reacted with mercury. However, chlorine desorption was evident at high $\ce{Cl-}$ and $\mathrm{pH}&lt;9$. Overall second-order reaction was observed between mercury and chlorine with an apparent second-order rate constant of $\pu{1.7\times 10^{15} M^{-1} s^{-1}}$ at $\pu{25 ^{\circ}C}$ and $\pu{1.4\times 10^{17} M^{-1} s^{-1}}$ at $\pu{55 ^{\circ}C}$. Gas-phase reaction was observed between $\ce{Hg}$  and $\ce{Cl2}$ on apparatus surfaces. Strong mercury absorption in water was also detected with $\ce{Cl2}$ present. Results indicate that the chlorine concentration, moisture, and surface area contribute positively to mercury removal.


I hope you will figured it out when you consider the standard reduction potentials of $\ce{Hg}$ and $\ce{OCl-}$ in any electrochemical series. For example, see Reference 2.

References:


L. L. Zhao, G. T. Rochelle, “Mercury absorption in aqueous hypochlorite,” Chemical Engineering Science 1999, 54(5), 655-662 (https://doi.org/10.1016/S0009-2509(98)00263-2).
S. G. Bratsch, “Standard Electrode Potentials and Temperature Coefficients in Water at $\pu{298.15 K}$,” Journal of Physical and Chemical Reference Data 1989, 18(1), 1-21 (https://doi.org/10.1063/1.555839).