Explanation:

Alright, let’s break it down, step by step:

- At 7:45 am, the minute hand is pointing East. That sets our orientation: East is where the minute hand points at 7:45.

- On a clock, the minute hand at 9 (45 mins) is pointing exactly left. So, we’re saying left on the clock is East.

- That means, on this clock, 12 is North, 3 is West, 6 is South, and 9 is East. This is a 90-degree clockwise shift of directions.

- The hour hand at 7:45 is between 7 and 8. In 3 hours, it’s 10:45. At 10:45, the hour hand is between 10 and 11.

- On this clock face, 10 is between (using our orientation) South (6) and West (3)—since directions are rotated, 10 sits between “South” and “West.”

Now, look at the options:

- Option 1: East — Not correct, not in that direction.

- Option 2: East-South — That’d be Southeast, not where 10 sits.

- Option 3: South — Nope, 10 isn’t at pure South (that'd be 6 o’clock).

- Option 4: North-East — Definitely not.

- The correct direction is between South and West, but the closest is South-West—which isn’t listed, but South is closer.

So, none of the options fit exactly, but if we had to pick the closest, South (Option 3) is as close as you get, but technically it's not perfect.

Option 3: South