1. **State the problem:** We have two numbers, say $a$ and $b$, and their product is $ab$. 2. **What is asked:** We want to find the increase in the product when the first number $a$ is increased by 4. 3. **Write the original product:** The original product is $$ab$$. 4. **Increase the first number by 4:** The new first number is $$a + 4$$. 5. **Calculate the new product:** The new product is $$(a + 4) \times b = ab + 4b$$. 6. **Find the increase in the product:** Increase = New product $-$ Original product $$= (ab + 4b) - ab = 4b$$. 7. **Answer:** The increase in the product is $4b$, which corresponds to option (a).