I have a question please help me with this.
Budgeted production 10,000 units
Actual production 15,000 units
Budgeted overhead cost $60,000
What is the overhead variance? Is it favorable or unfacorable?

It isn't a question of favourable or unfavourable because you have nothing to compare it to. All you have is a variation in the number of units of production. We don't know if the overhead is variable or fixed or mixed so we cannot calculate a variance. If it entirely variable there is no variance. Read the book.