Is it permissible to take the extra amount (4,0) that I saved by finding a mechanical engineer at a lower price than the director specified (6,0), or must I inform the director of this?

You must inform the manager of the truth regarding the engineer's cost, and you may request a commission for finding him. If he refuses, you are not permitted to lie or wrongfully take company money. You must inform the manager of the true agreed-upon wage with the engineer, which is two thousand, not six thousand.