1. The problem is to add the numbers: $\frac{1}{3}$, $-0.6$, $-1.2$, and $-\frac{1}{4}$.\n\n2. First, convert all numbers to fractions or decimals for easier addition.\n- $\frac{1}{3}$ is approximately $0.3333$.\n- $-0.6$ is already a decimal.\n- $-1.2$ is already a decimal.\n- $-\frac{1}{4}$ is $-0.25$.\n\n3. Now add all decimals: $$0.3333 + (-0.6) + (-1.2) + (-0.25)$$\n\n4. Perform the addition step-by-step:\n$$0.3333 - 0.6 = -0.2667$$\n$$-0.2667 - 1.2 = -1.4667$$\n$$-1.4667 - 0.25 = -1.7167$$\n\n5. The sum of the numbers is approximately $-1.7167$.\n\n6. To express the answer as a fraction, note that $-1.7167$ is close to $-\frac{43}{25}$ (since $\frac{43}{25} = 1.72$).\n\nFinal answer: $$\boxed{-1.7167 \approx -\frac{43}{25}}$$