The sum of two numbers is 42. the smaller number is 6 less than the larger number. what are the numbers?

 The 2 (TWO) numbers are:  18 and 24 .

Explanation:

 x + y = 42 ;   Let "x" be the 'smaller number' ;  "y'' be the "larger number";  

so:  x = y − 6 ;

Now, substitute "y−6" for "x" in the equation:

   x + y = 42 ;

     y − 6 + y = 42 

            Combine the "like terms", which appear on the left-hand side of the equation:

 y + y , =  2y ;   and rewrite the equation:

          2y − 6 = 42 ;

Now, add "6" to each side of the equation:

          2y − 6 + 6 = 42 + 6 ;

  to get:   2y = 48 ;

            Now, divide EACH side of the equation by "2";  to isolation "y" on one side of the equation; and to solve for "y" ;

              2y / 2  =  48 / 2 ;

to get:  y = 24 ; which is the value of one of the number we which to solve for —specifically, the larger number.

Now, we can use one of two methods to solve for "x".   In fact, let us use BOTH methods, to ensure we have the same value for "x" (which serves a purpose for confirming our answer and checking our work).  We can start with EITHER method, first in EITHER ORDER; nonetheless, I shall still list them as "Method 1" and "Method 2"—as follows:

Method 1)
           From the original problem,  "The smaller number is 6 less than the smaller number" ;  or:   " x =  y − 6 " .

            Since our obtained/ solved value for "y" is "24" ;  we can plug in the value, "24", for "y"; into this equation; and solve for "x" ;

                x = y − 6  = 24 - 6 ; 
 
 to get:    x = 18 .  which is the other value we wish to obtain, the "smaller number" value.

Method 2)
         From the original problem:  "The sum of two numbers is 42. " ; 

 or, " x + y = 42 " .

     Using our obtained/solved value for "y", which is: "24", we can plug this value, "24", for "y", into the above equation; and solve for "x";

       x +  y = 42 ;  

       x + 24 = 42 ;

Now, subtract "24" from EACH side of the equation, to isolate "x" on one side of the equation; and to solve for "x" ;

      x + 24 − 24  =  42 − 24 ;

            x = 18 ;  which is the same value we got for "x" from:  "Method 1" above.

So, the two numbers are:  "18" and "24".   Do they add up to "42"?

18 + 24 =? 42?? Yes.  

Is the "smaller number" (18) , "6 less than the larger number (24)?

Does 18 + 6 =?  24 ??  Yes!   Does 24 − 6 =? 18 ??  Yes!

So the two (2) numbers are:    18 and 24 .