You ought to fix what Alvaro mentioned - this will not only make your code shorter and easier to handle, but it will add the additional possibility of using a board with more than 6 rows.

About checking whether there are number pieces in a row/column/diagonally you could try this:

//Let's say you just put a new piece with coordinates x,y and it's color is col then:
if( countPieces(x,y,col, -1, 0) + countPieces(x,y,col, 1, 0) - 1 >= number )
{
   //4 in a row
}
if( countPieces(x,y,col, 0, -1) + countPieces(x,y,col, 0, 1) - 1 >= number )
{
   //4 in a column
}
if( countPieces(x,y,col, 1, 1) + countPieces(x,y,col, -1, -1) - 1 >= number )
{
   //4 diagonally
}
if( countPieces(x,y,col, -1, 1) + countPieces(x,y,col, 1, -1) - 1 >= number )
{
    //4 diagonally
}

What this does is basically check the number of pieces left of your new piece with color == col then adds this number with the number of pieces right of your new piece with color == col and subtracts 1 because we counted the new piece twice. If this number proves to be higher or equal to number(=4) then we have 4 or more pieces in the row with the same color. Analogically for the other cases.

bool Board::is_last_move_a_win(int x, int y) const {
  int dx_table[4] = {1, 0, 1, -1};
  int dy_table[4] = {0, 1, 1, 1};
  
  for (int d = 0; d < 4; ++d) {
    int dx = dx_table[d];
    int dy = dy_table[d];
      if(countPieces(x, y, dx, dy) + countPieces(x, y, -dx, -dy) >= 3)
        return true;
  }
  
  return false;
}