I'll stat with a quick rundown of what dilution something actually means.
In simple terms, molarity is a measure of how concentrated a solution is in terms of the amount of solute it contains per liter of solution.
When your aim is to dilute a solution, you're essentially keeping the amount of solute constant while increasing the volume of the solution.
This can be written as
#color(blue)( overbrace(c_1 xx V_1)^(color(purple)("moles of solute in initial solution")) = overbrace(c_2 xx V_2)^(color(purple)("moles of solute in target solution")))#
Notice that you can rewrite this equation as
#c_1/c_2 = V_2/V_1#
The ratio between the volume of the target solution and the volume of the initial solution gives you the dilution factor.
#color(blue)("D.F". = V_"final"/V_"initial")#
For example, in order to perform a
#c_2 = 1/2 * c_1#
will give you
#V_2/V_1 = (color(red)(cancel(color(black)(c_1))))/(1/2 * color(red)(cancel(color(black)(c_1)))) = 2#
Notice that you don't need concentration values to find the dilution factor of a solution, as is the case with your example.
In your case, you want to perform a
#"D.F." = 64 = V_2/V_1#
This tells you that the volume of the target solution must be
#64 = V_2/V_1 implies V_2 = 64 * V_1#
Plug in your value for the volume of the aliquot to get
#V_2 = 64 * "1.194 mL" = "76.416 mL"#
Since the volume of the target solution will be equal to
#V_2 = V_1 + V_"saline"#
it follows that you will need to add
#V_"saline" = "76.416 mL" - "1.194 mL" = color(green)(color(green)("75.22 mL")#
of sterile saline solution to your anti-cancer drug to perform a