On a Prompt page, create a parametized filter on Project Type.
Then create a parametized filter on Project Name; and on the fourth window of the wizard (Populate Control) select Project Type using the Cascading Source drop down box. You then may wish to select the value prompt produced and change the Select UI in the Properties pane to List Box.
Then from the Insertable Objects pane drag a Prompt Button and drop it between Next> and Finish buttons at the bottom of the Prompt page. Select this new button ("Next>" probably) You then need to change the button type to Reprompt using the Properties pane under General -->Type.
Run the report, select a Project Type(s) and hit the Reprompt button; a list of Project Names of the selected Project Type should appear in the Project Names prompt.