Extract Values from a Table

I need help, have to extract a project billing hours from a very large table.

Rows contain employee names & columns are project name
What I need is , when I change the employee name, I need to extract how many hours for each project that employee has billed.
Since this is a very large table with more than 200 columns. Is there a formula where i can extract only columns with billed hours?
I'm attaching the sample sheet.

Thank you in advance