This analysis evaluates the characteristics of conventional nanofluid heat transfer with those of emerging hybrid nanofluid. Hybrid nanofluid, a new type of conventional fluid, has been used toward the enhancement of heat transfer in the boundary layer flow. This research also prompts that 0.001 solid volume fraction of Gold (Au) is fixed, then consequently, various solid volume fractions of Molybdenum disulfide (Mo) are added into the mixture with water as the base fluid to form Au - Mo/water hybrid nanofluid. Using the necessary similarity variables, the governing non-linear partial differential equations are resolved into a system of coupled ordinary non-linear differential equations. The transformed equations are numerically solved by employing the Runge-Kutta Fehlberg method with shooting technique. The numerical parametric analysis, which has been conducted to explore the effects of different physical parameters involved in the problem, provides comparisons. The present problem is new, original, with many substantial findings in the current industry for practical problems. It is found that dual solutions exist up to a certain value of the decreases as nanoparticle volume fractions for Molybdenum disulfide increase.