Refer to figure.
In the southern hemisphere, low-pressure systems (cyclones or depressions) produce clockwise wind circulation due to the Coriolis force deflecting air to the left. Air converges toward the low-pressure centre from all directions driven by the pressure gradient force. The Coriolis force (leftward in SH) deflects this inward-flowing air to produce a clockwise spiral converging toward the low-pressure centre. 

A useful memory tool: in the SH, low pressure rotates CLOCKWISE (same direction as clock hands when viewed from above); high pressure rotates ANTI-CLOCKWISE.

Clockwise, with the area of lowest pressure in the centre → CORRECT. In the southern hemisphere, cyclonic (low-pressure) circulation is clockwise. The centre of the low contains the lowest pressure, which is the defining characteristic of a low-pressure system.

Anti-clockwise, with the area of lowest pressure in the centre → INCORRECT. Anti-clockwise cyclonic circulation with lowest pressure in the centre describes a NORTHERN HEMISPHERE low. In the southern hemisphere the same low rotates clockwise. The pressure distribution is correct but the rotation direction applies to the wrong hemisphere.

Clockwise, with the area of highest pressure in the centre → INCORRECT. Clockwise rotation in the southern hemisphere is correctly identified as the SH low circulation. However the highest pressure at the centre describes an anticyclone (high), not a low. A low has lowest pressure at the centre by definition.

Anti-clockwise, with the area of highest pressure in the centre → INCORRECT. Anti-clockwise rotation with highest pressure at the centre describes a SOUTHERN HEMISPHERE HIGH (anticyclone). This option combines the rotation of an SH high with the pressure distribution of an SH high, but is being asked about a low-pressure system.