We propose a scenario to understand the puzzling features of the recent experiment by Kang and coworkers on tunneling between laterally coupled quantum Hall liquids by modeling the system as a pair of coupled chiral Luttinger liquid with a point contact tunneling center. We show that for filling factors $ν∼1$ the effects of the Coulomb interactions move the system deep into strong tunneling regime, by reducing the magnitude of the Luttinger parameter $K$, leading to the appearance of a zero-bias differential conductance peak of magnitude $G_t=Ke^2/h$ at zero temperature. The abrupt appearance of the zero bias peak as the filling factor is increased past a value $ ν^* \gtrsim 1$, and its gradual disappearance thereafter can be understood as a crossover controlled by the main energy scales of this system: the bias voltage $V$, the crossover scale $T_K$, and the temperature $T$. The low height of the zero bias peak $∼ 0.1e^2/h$ observed in the experiment, and its broad finite width, can be understood naturally within this picture. Also, the abrupt reappearance of the zero-bias peak for $ν \gtrsim 2$ can be explained as an effect caused by spin reversed electrons, \textit{i. e.} if the 2DEG is assumed to have a small polarization near $ν∼2$. We also predict that as the temperature is lowered $ν^*$ should decrease, and the width of zero-bias peak should become wider. This picture also predicts the existence of similar zero bias peak in the spin tunneling conductance near for $ν \gtrsim 2$. ; Comment: 17 pages, 8 figures