Find Highest Match from Another Column

Hello,

I would like to use Excel formulas (not VBA code) to select the highest number from the corresponding column that matches the value given. I have attached a file as an example:

Say the value/name I am interested is 'Lee'. As shown on the attached, the highest number associated with Lee is 3. Hence, I would need the value 3 to be returned.
Say the value/name I am interested is 'Paul'. As shown on the attached, the highest number associated with Paul is 4. Hence, I would need the value 4 to be returned.

I have been pulling my hair out with this one, so if anyone can help it will be very much appreciated!

Many thanks!

Lee