The NaOH and the red dye will not react between them, so, the process that it's occurring is only a dilution. The final volume of the solution will be the volume of the flask, which is 100 mL.
The number of moles (n) of each substance will not vary, and it's calculated by the multiplication of the concentration (C) by the volume (V). If 1 is the initial solution, and 2 the diluted: