incompatible types: String cannot be converted to char tile += tiles;

The solution should look like this.

public void addTile(char tile) {
    // TODO: Add the tile to tiles
    tiles += tile;
    // which is the same as
    // tiles = tiles + tile;
  }

  public boolean hasTile(char tile) {
    // TODO: Determine if user has the tile passed in
    return tiles.indexOf(tile) != -1;
  }

In the first method addTile, you need to add the char variable tile which is passed as a parameter to the method to the variable tiles, which is a class/instance variable of type String. So, you use the shortened version for concatenating strings (and chars) += to simply add the passed tile to the tiles. Does it make more sense?

In the second method hasTile, you need to return a boolean (true or false) stating if a char tile is present in the String tiles. So, you return whether tile is contained in the tiles by using the above return statement. What it does, is check if the char is present in the String by using the indexOf method on the String and passing that char as a parameter (inside parenthesis). What that method returns is the index (location) of the char within the String if it's present, or -1 if it isn't. Therefore if we get any number which is not -1 (it can be 1, 5, 17 or anything else, we don't care), then our return statement will be true and the method hasTile will return true, meaning the char was present. If the result of the indexOf method is actually -1, that means that the char was not present in the String and our statement will then evaluate to false, since -1 is not equal to -1 is actually false.

Hope this cleared things up.