We investigate the molecular mechanism underlying the liquid-phase exfoliation of graphene in aqueous/N-methyl-2-pyrrolidone (NMP) solvent mixtures and calculate the associated free energies, considering different NMP concentrations and exfoliation temperatures. We employ steered molecular dynamics to establish a path for the exfoliation of a graphene sheet from graphite within each solvent environment. Then, we conduct umbrella sampling simulations throughout the created paths to compute the potential of mean force (PMF) of the graphene sheet. As the exfoliated nanosheet disperses into the liquid, it becomes fully covered by an adsorbed solvent monolayer. We analyze the composition of the monolayer by measuring the direct contacts of either NMP or water molecules with the carbon surface. The carbon surface exhibits a preference for adsorbing NMP over water. The NMP molecules form a hydrophobic compact monolayer structure, effectively protecting the carbon interface from unfavorable interactions with water. The creation of the hydrophobic monolayer is a key factor in the exfoliation process, as it effectively inhibits the restacking of exfoliated nanosheets. An adequate level of graphene solubility is achieved through the addition of 20 % to 30 % water by weight to the NMP solvent. This finding holds significant importance for improving production efficiency and reducing dependence on organic solvents in the industrial manufacturing of graphene.