A

Step 1: Identify the velocities of the bodies:
\( \vec{V_A} = (2ti + 6j) \) m/s
\( \vec{V_B} = (3i + 4j) \) m/s
\( \vec{V_C} = (6i - 4tj) \) m/s

Step 2: Calculate the relative velocity of A with respect to B:
\( \vec{V_{A/B}} = \vec{V_A} - \vec{V_B} = (2ti + 6j) - (3i + 4j) = (2t - 3)i + (6 - 4)j = (2t - 3)i + 2j \)
This is not zero unless t is a specific value.

Step 3: Calculate the relative velocity of B with respect to C:
\( \vec{V_{B/C}} = \vec{V_B} - \vec{V_C} = (3i + 4j) - (6i - 4tj) \)
= \( (3 - 6)i + (4 + 4t)j = -3i + (4 + 4t)j \)
This is along the negative x-axis.

Step 4: Calculate the relative velocity of A with respect to C:
\( \vec{V_{A/C}} = \vec{V_A} - \vec{V_C} = (2ti + 6j) - (6i - 4tj) \)
= \( (2t - 6)i + (6 + 4t)j \)
This gives positive and negative components in both directions.

Step 5: Calculate relative velocity of C with respect to A:
\( \vec{V_{C/A}} = \vec{V_C} - \vec{V_A} = (6i - 4tj) - (2ti + 6j) \)
= \( (6 - 2t)i + (-4t - 6)j \)
This can also give components in both directions.

Summary:
- (i) on A w.r.t B: not zero
- (ii) on B w.r.t C: along negative x-axis
- (iii) on A w.r.t C: depends on t
- (iv) on C w.r.t A: components will vary
Hence, matching is A: [A]-zero, [B]-along negative x-axis, [C]-along positive y-axis, [D]-along negative y-axis.