First I would index through the first array using a for loop and for each of the elements in the first loop, you can multiply it by a random element of the 2nd element. Afterwards, set the multiplication back to the original x array.
The code would be:
//using the Random Class from Java (http://docs.oracle.com/javase/6/docs/api/java/util/Random.html#nextInt())
import java.util.Random;
public class randomArrayMultiplication {
public static void main(String [] args) {
int[] x = {1,2,3,4,5};
int[] y = {1,3,12};
//declare a new random class
Random rn = new Random();
//iterate through the first array
for (int i = 0; i < x.length; i ++) {
//for every element of the x array multiply it by a random
//element in the y array (using the randomInt method from the
//random class in which " Returns a pseudorandom, uniformly
//distributed int value between 0 (inclusive) and the specified
//value (exclusive), drawn from this random number generator's
//sequence."). Therefore, we will choose a random element in
//the y array and multiple it by the x array. At the same time,
//we will end up setting that back to the x array so that every
//array in x is multiplied by a random element in y.
x[i] = x[i] * y[rn.nextInt(y.length)];
}
}
}