While we're not supposed to give you answers to homework on these boards, I can guide you in the right direction.
Use your dimensional analysis to set up your equation to solve this. You know you need to end up with mcg. Start with your given 25 mcg/kg. That leaves kg on the bottom of your fraction. Next multiply by the ratio of kilograms to pounds. That leaves pounds on the bottom of your fraction. Finally, multiply by 143 pounds/1 patient. This leaves you with micrograms/patient, which is what you want your dose to be. By writing down all labels to each step in the dimensional analysis and crossing them off as you eliminate them by multiplication, you can easily determine if you have the correct answer.