1. The problem is to simplify the expression: $$2(a + 2b) + 2b$$. 2. Use the distributive property: $$2(a + 2b) = 2 \times a + 2 \times 2b = 2a + 4b$$. 3. Now add the remaining term: $$2a + 4b + 2b$$. 4. Combine like terms: $$4b + 2b = 6b$$. 5. The simplified expression is: $$2a + 6b$$. This means the expression $$2(a + 2b) + 2b$$ simplifies to $$2a + 6b$$.