Preview:
private TilePane selectedTilePane;
private TilePane currentTilePane;
private ImageView selectedImageView;

void onMouseClicked(MouseEvent event) {
  this.resetTileBackgroundColor();
  this.selectedImageView = (ImageView) event.getSource();
  this.selectedTilePane = (TilePane) this.selectedImageView.getParent();
  this.selectedTilePane.setStyle("-fx-background-color:gray");

}

void onMouseEntered(MouseEvent event) {
  this.currentTilePane = (TilePane) event.getSource();
  if (!this.currentTilePane.equals(this.selectedTilePane)) {
    this.currentTilePane.setStyle("-fx-background-color:lightgray");
  }
}

void onMouseExited(MouseEvent event) {
  this.currentTilePane = (TilePane) event.getSource();
  if (!this.currentTilePane.equals(this.selectedTilePane)) {
    this.currentTilePane.setStyle("-fx-background-color:whitesmoke");
  }
}

private void resetTileBackgroundColor() {
  tilePane<XXXXX>.setStyle("-fx-background-color:whitesmoke");
}
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