John has a garden with dimensions 7 feet long x 6 feet wide. He wants to enlarge the garden to an area of 108 square feet. How much farther will he need to extend the length of the garden to attain his desired area?

The current area of the garden is 7 feet * 6 feet = <<7*6=42>>42 square feet.

The difference in the area desired and the current area is 108 square feet - 42 square feet = <<108-42=66>>66 square feet.
John will need to extend the length of the garden 66 square feet / 6 feet (width) = <<66/6=11>>11 feet. Answer: \boxed{11}.