A 3.8 cm -thick layer of oil is sandwiched between a 1.7 cm -thick sheet of glass and a 2.4 cm -thick sheet of polystyrene plastic.?

The trouble with this question is that the terms "glass" and "oil" aren't specific enough to tell us what the refractive index of either one of them might be.  Your textbook probably contains a list of refractive index values, and you should use whatever THEY show as the refractive index of "glass" and of "oil."  I'll use 1.5 for glass and 1.4 for oil.  For polystyrene, I'll use 1.6 although that too is somewhat variable.

OK, so if those refractive indexes are correct, the time in seconds would be

(1.7 x 10^(-2) m * 1.5)/(3.00 x 10^8 m/s) +

(3.8 x 10^(-2) m * 1.4)/(3.00 x 10^8 m/s) +

(2.4 x 10^(-2) m * 1.6)/(3.00 x 10^8 m/s)

= (2.55 + 5.32 + 3.84) x 10^(-10) s divided by 3

= 1.171 x 10^(-9) s divided by 3

= 0.39 nanoseconds.

You can repeat the calculations if you have been given specific values for the refractive indices.