The correct answer is (a) South-East.
At 4 o’clock, the hour hand is pointing between 3 and 4, which is $\frac{1}{4}$ of the way around the clock. The minute hand is pointing to 12, which is $\frac{12}{60}$ of the way around the clock. The ratio of the hour hand’s position to the minute hand’s position is $\frac{1}{4}:\frac{12}{60} = \frac{1}{15}$. This means that the hour hand is $\frac{1}{15}$ of the way between 3 and 4, which is $\frac{1}{15} \times 90^\circ = 6^\circ$. Since the hour hand is pointing between 3 and 4, which are on the east side of the clock, the hour hand is pointing $\boxed{\text{South-East}}$.
Option (b) is incorrect because the hour hand is not pointing to the north-east. Option (c) is incorrect because the hour hand is not pointing to the south-west. Option (d) is incorrect because the hour hand is not pointing to the north-west.