Step 1 :Given the probability of Elise having a quiz is 0.46 and Ella having a quiz is 0.38, we can find the probability of both having a quiz on the same day by multiplying the individual probabilities since the events are independent: \(0.46 \times 0.38\)
Step 2 :Calculating the product, we get \(0.46 \times 0.38 = 0.1748\). Therefore, the probability that Elise and Ella will have a quiz on the same day is \(\boxed{0.1748}\)