Looking up information in one worksheet and deleting information if it isn't there

Hi - I'm new to this, so please be patient with me. I know enough about Excel to be dangerous. To my problem.

I have created a worksheet for our company's accounting department for them to show a cost to complete on our projects. The information varies from project to project, so I need to find a way to search through one worksheet with the right information and transfer the information to the other worksheet and if it is not there then delete the row. I have attached both copies of the worksheets for a better understanding of what is needed. I would appreciate any help.