You need your target solution to have a concentration of #"0.6 g/mL"#, which means that every milliliter of solution must contain #"0.6 g"# of sugar.
Simply put, you need to make sure that you dissolve enough sugar in that #"150-mL"# sample of water to ensure that every milliliter of solution will contain #"0.6 g"# of sugar.
Well, if you need #"1 mL"# to contain #"0.6 g"#, then #"150 mL"# must contain
#150 color(red)(cancel(color(black)("mL solution"))) * overbrace("0.6 g sugar"/(1color(red)(cancel(color(black)("mL solution")))))^(color(blue)("given concentration")) = color(green)("90 g sugar")#
You can dissolve about #"2 g"# of sugar per milliliter of water at room temperature, so you could prepare this solution by dissolving #"90 g"# of sugar in about #"100 mL"# of water, then adding enough water to get the final volume of the solution to #"150 mL"#.
