Explanation:

Let's represent the seven positions in the queue from left to right as $P_1, P_2, P_3, P_4, P_5, P_6, P_7$. 1. **"E is at the fifth place from left."** $P_1 \ P_2 \ P_3 \ P_4 \ \mathbf{E} \ P_6 \ P_7$ 2. **"G is at the first place from right."** This means G is at the seventh position from the left ($P_7$). $P_1 \ P_2 \ P_3 \ P_4 \ \mathbf{E} \ P_6 \ \mathbf{G}$ 3. **"B is three places after F."** This implies that if F is at position $x$, B is at position $x+3$. So, there are two people between F and B ($F \_ \_ B$). Let's test possible positions for F and B: * If F is at $P_1$, then B is at $P_4$. This gives: $\mathbf{F} \ P_2 \ P_3 \ \mathbf{B} \ \mathbf{E} \ P_6 \ \mathbf{G}$ * If F is at $P_2$, then B is at $P_5$. This conflicts with E being at $P_5$. * If F is at $P_3$, then B is at $P_6$. This gives: $P_1 \ P_2 \ \mathbf{F} \ P_4 \ \mathbf{E} \ \mathbf{B} \ \mathbf{G}$ 4. **"Only C is between A and B."** This means A, C, and B must be in a consecutive block, either $A \ C \ B$ or $B \ C \ A$. \nLet's evaluate the two promising scenarios for F and B: **Scenario 1: F at $P_1$, B at $P_4$**\nQueue so far: $\mathbf{F} \ P_2 \ P_3 \ \mathbf{B} \ \mathbf{E} \ P_6 \ \mathbf{G}$\nRemaining children to place: A, C, D.\nRemaining empty slots: $P_2, P_3, P_6$. \nNow apply "Only C is between A and B":\nSince B is at $P_4$, the sequence $A \ C \ B$ would mean A is at $P_2$ and C is at $P_3$. This fits perfectly. \nResulting queue: $\mathbf{F} \ \mathbf{A} \ \mathbf{C} \ \mathbf{B} \ \mathbf{E} \ P_6 \ \mathbf{G}$ \nThe children placed are F, A, C, B, E, G. The only remaining child is D. The only remaining empty slot is $P_6$. \nFinal arrangement: $\mathbf{F} \ \mathbf{A} \ \mathbf{C} \ \mathbf{B} \ \mathbf{E} \ \mathbf{D} \ \mathbf{G}$ \nLet's verify all conditions with this arrangement: * E is at the fifth place from left: Yes, E is at $P_5$. * Only C is between A and B: Yes, A is at $P_2$, C is at $P_3$, B is at $P_4$. C is between A and B. * G is at the first place from right: Yes, G is at $P_7$. * B is three places after F: Yes, F is at $P_1$, B is at $P_4$.\nAll conditions are satisfied. **Scenario 2: F at $P_3$, B at $P_6$**\nQueue so far: $P_1 \ P_2 \ \mathbf{F} \ P_4 \ \mathbf{E} \ \mathbf{B} \ \mathbf{G}$\nRemaining children to place: A, C, D.\nRemaining empty slots: $P_1, P_2, P_4$. \nNow apply "Only C is between A and B":\nSince B is at $P_6$, for $A \ C \ B$ or $B \ C \ A$ to fit, A and C would need to be at $P_4, P_5$ or $P_5, P_7$. However, $P_5$ is occupied by E, and $P_7$ by G. This scenario does not allow for A, C, B to be placed consecutively with C between A and B. \nTherefore, Scenario 1 is the correct arrangement. \nIn the final arrangement $\mathbf{F} \ \mathbf{A} \ \mathbf{C} \ \mathbf{B} \ \mathbf{E} \ \mathbf{D} \ \mathbf{G}$, D is at the sixth position from the left. * Option A (sixth): This matches our finding. * Option B (fourth): This is the position of B. * Option C (second): This is the position of A. * Option D (third): This is the position of C. \nThus, the position of D from the left is sixth.