1. **State the problem:** Solve the equation $$-3(4x - \sqrt{2}) = -12x + \sqrt{4}.$$\n\n2. **Rewrite the equation:** Distribute the $-3$ on the left side:\n$$-3 \times 4x + (-3) \times (-\sqrt{2}) = -12x + \sqrt{4}$$\nwhich simplifies to\n$$-12x + 3\sqrt{2} = -12x + 2.$$\n\n3. **Analyze the equation:** Both sides have $-12x$, so subtract $-12x$ from both sides:\n$$3\sqrt{2} = 2.$$\n\n4. **Evaluate the constants:** $\sqrt{2} \approx 1.414$, so\n$$3 \times 1.414 = 4.242,$$ which is not equal to 2.\n\n5. **Conclusion:** Since $3\sqrt{2} \neq 2$, the equation has no solution.\n\n**Final answer:** There is no value of $x$ that satisfies the equation.\n