1. **State the problem:** Solve for $t$ in the equation $$\frac{7}{12} \times \frac{t}{5} \times \frac{1}{3} = \frac{14}{45}.$$\n\n2. **Write the equation clearly:** $$\frac{7}{12} \cdot \frac{t}{5} \cdot \frac{1}{3} = \frac{14}{45}.$$\n\n3. **Multiply the fractions on the left side (except $t$):**\n$$\frac{7}{12} \times \frac{1}{3} = \frac{7 \times 1}{12 \times 3} = \frac{7}{36}.$$\nSo the equation becomes $$\frac{7}{36} \times \frac{t}{5} = \frac{14}{45}.$$\n\n4. **Combine the fractions on the left:**\n$$\frac{7}{36} \times \frac{t}{5} = \frac{7t}{180}.$$\nSo, $$\frac{7t}{180} = \frac{14}{45}.$$\n\n5. **Solve for $t$ by cross-multiplying:**\n$$7t \times 45 = 14 \times 180.$$\n\n6. **Calculate each side:**\n$$315t = 2520.$$\n\n7. **Divide both sides by 315 to isolate $t$:**\n$$t = \frac{2520}{315}.$$\n\n8. **Simplify the fraction:**\n$$t = 8.$$\n\n**Final answer:** $$t = 8.$$