To simplify the expression $c(3c^5 + c + b - 4)$, we distribute $c$ to each term inside the parentheses:

1. Multiply $c$ with $3c^5$:
   $c \cdot 3c^5 = 3c^6$

2. Multiply $c$ with $c$:
   $c \cdot c = c^2$

3. Multiply $c$ with $b$:
   $c \cdot b = bc$

4. Multiply $c$ with $-4$:
   $c \cdot -4 = -4c$

Thus, the simplified expression is: $3c^6 + c^2 + bc - 4c$

The answer in the boxes should be filled as follows:

• First box: $3$ (for $3c^6$)
• Second box: $2$ (for $c^2$)
• Third box: $-4$ (for $-4c$)

Would you like more details or have questions about the steps?

Here are some related questions for further exploration:

1. How do you distribute a monomial across terms in a polynomial?
2. What is the general process for simplifying expressions with multiple variables?
3. How does exponent multiplication work when distributing terms?
4. Can distribution be used for simplifying complex expressions in algebra?
5. What happens when a term with a negative sign is distributed?

Tip: Always check each term individually when distributing to ensure accurate simplification.