Answer:
The method is as follows:
 public static void checkIntersection(double x1, double y1, double r1, double x2, double y2, double r2){
     double d = Math.sqrt(Math.pow((x1 - x2),2) + Math.pow((y1 - y2),2));
     if(d == r1 + r2){
         System.out.print("The circles touch each other");     }
     else if(d > r1 + r2){
         System.out.print("The circles do not touch each other");     }
     else{
         System.out.print("The circles intersect");     }
 }
Explanation:
This defines the method
 public static void checkIntersection(double x1, double y1, double r1, double x2, double y2, double r2){
This calculate the distance
     double d = Math.sqrt(Math.pow((x1 - x2),2) + Math.pow((y1 - y2),2));
If the distance equals the sum of both radii, then the circles touch one another
<em>     if(d == r1 + r2){</em>
<em>         System.out.print("The circles touch each other");     }</em>
If the distance is greater than the sum of both radii, then the circles do not touch one another
 <em>    else if(d > r1 + r2){</em>
<em>         System.out.print("The circles do not touch each other");     }</em>
If the distance is less than the sum of both radii, then the circles intersect
<em>    else{</em>
<em>         System.out.print("The circles intersect");     }</em>
 }