No. The second for loop is trying to use a variable j
that is not defined at that point.
(The first for statement  declares a j
than can only be seen within that loop.)
class sameName
{
  public static void main ( String[] args )
  {
    int sumEven = 0;
    int sumOdd  = 0;
    for ( int j = 0;  j < 8; j=j+2 )
        sumEven = sumEven + j;
    System.out.println( "The sum of evens is: " + sumEven ); 
    for ( j = 1;  j < 8; j=j+2 )    //  "j" can not be seen at this point.
        sumOdd  = sumOdd + j;                     
    System.out.println( "The sum of odds is: " + sumOdd );
  } 
}
Here is another version of the program, which is syntactically correct, but is not nicely done.
class foolishTypist
{
  public static void main ( String[] args )
  {
    int sumEven = 0;
    int sumOdd  = 0;
    int j;     // Same "j" used for both loops.
    for ( j = 0;  j < 8; j=j+2 )
        sumEven = sumEven + j;
    System.out.println( "The sum of evens is: " + sumEven ); 
    for ( j = 1;  j < 8; j=j+2 ) 
        sumOdd  = sumOdd + j;                     
    System.out.println( "The sum of odds is: " + sumOdd );
  } 
}
It is best to keep sections of code self-contained. With this (foolish) version, both loops depend on something distant from themselves. Although this program is clear enough, a longer program might be harder to understand. Here, for instance, is a typical hard to understand program:
class foolishTypist
{
  public static void main ( String[] args )
  {
    int sumEven = 0;
    int sumOdd  = 0;
    int j = 0;
    int i = 1;
    for ( j = 0;  j < 8; j=j+2 )
        sumEven = sumEven + j;
    System.out.println( "The sum of evens is: " + sumEven ); 
    for ( i = 1;  i < 8; i=i+2 ) 
        sumOdd  = sumOdd + j;                     
    System.out.println( "The sum of odds is: " + sumOdd );
  } 
}