1. **State the problem:** We need to find the numbers that go in the two red square boxes in the equation: $$2(\square - 4x) + \square(3x - 1) = 2(2x + 3)$$ 2. **Rewrite the equation with variables:** Let the first box be $a$ and the second box be $b$. The equation becomes: $$2(a - 4x) + b(3x - 1) = 2(2x + 3)$$ 3. **Expand both sides:** $$2a - 8x + 3bx - b = 4x + 6$$ 4. **Group like terms:** Group $x$ terms and constants: $$(-8x + 3bx) + (2a - b) = 4x + 6$$ 5. **Equate coefficients of $x$ and constants:** For $x$ terms: $$-8 + 3b = 4$$ For constants: $$2a - b = 6$$ 6. **Solve for $b$ from the $x$ terms equation:** $$3b = 4 + 8 = 12$$ $$b = \frac{12}{3} = 4$$ 7. **Substitute $b=4$ into constants equation:** $$2a - 4 = 6$$ $$2a = 10$$ $$a = \frac{10}{2} = 5$$ 8. **Final answer:** The first box is $5$ and the second box is $4$. $$\boxed{5} \text{ and } \boxed{4}$$