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)];
    }
  }
}