Hi,
There is no option to do that.
You can configure an option to your product so that the customer can select or not the option and that will automatically add the price of the option to the product price.
You can also configure a custom item field for customers to enter a text on your product page.
There is however no system to link the display of a custom field with the value selected in an option.
That could be done with a customization of the code of the file "option" of the view "product" via the menu Display>Views in order to add custom javascript to hide or display the custom field when the option dropdown value is changed.