D15 Answer

The easiest way to do this is to regard the array as a linear sequence in memory:

int rotateDownN ( int x[][NumColumns], int nrows, int N )
{
  int j ;

  /* If N is out of range, return 0 */
  if ( N < 0 || N > nrows*NumColumns) return 0;

  /* Save the first N entries */
  int temp[N];
  for ( j=0; j<N; j++ ) temp[j] = x[0][j];

  /* Slide elements down */
  for ( j=0; j<nrows*NumColumns-N; j++ )
    x[0][j] = x[0][j+N];

  /* Copy first N entries to last N positions */
  for ( j=0; j<N; j++ )
    x[0][nrows*NumColumns-N+j] = temp[j];

  return 1;
}

Remark: Many C compilers will not allow a local array variable with a size that depends the the value of a parameter:

  int temp[N];

With such a compiler, the function must explicitly allocate and deallocate memory to hold the temporaries:

int rotateDownNmalloc ( int x[][NumColumns], int nrows, int N )
{
  int  j ;
  int *temp;

  if ( N < 0 || N > nrows*NumColumns) return 0;

  temp = (int *)malloc( N*sizeof( int ) );

  for ( j=0; j<N; j++ ) temp[j] = x[0][j];

  for ( j=0; j<nrows*NumColumns-N; j++ )
    x[0][j] = x[0][j+N];

  for ( j=0; j<N; j++ )
    x[0][nrows*NumColumns-N+j] = temp[j];

  free ( temp );
  return 1;
}

It is possible to write this function without using any additional storage (other than a few index variables and one temporary.) But this method is complicated and offers no speed advantage.