With reference to the figure given below, the number of different routes from S to T without retracing from U and/or V, is

To solve this, I will break the journey from S to T into three stages based on the connecting points U and V.\n\n1. **Stage 1 (S to U):** Looking at the first section, there are 3 distinct paths to get from S to U (an upper path, a middle straight line, and a lower path).\n\n2. **Stage 2 (U to V):** Looking at the middle section, it is different from the first. There is an upper path and a lower path, but *no* middle straight line. So, there are only 2 paths here.\n\n3. **Stage 3 (V to T):** The final section looks identical to the first, with an upper path, a middle straight line, and a lower path. So, there are 3 paths.\n\nSince these are independent stages and we need to go from S to U *and then* U to V *and then* V to T, we apply the multiplication rule:\nTotal Routes = (Ways for S-U) × (Ways for U-V) × (Ways for V-T)\nTotal Routes = 3 × 2 × 3 = 18.\n\nThis matches option (D).