Potential difference across the capacitor (steady state)

In steady state (DC), the capacitor behaves as an open circuit

no current flows through it.
So the circuit reduces to two parallel branches between the left and right terminals:
Top branch

Voltage drop across left 4Ω:

Potential at top node:

Bottom branch

Voltage drop across left 4Ω:

Potential at bottom node:

Voltage across capacitor

Discharge current when switch S is opened

When S is opened, the battery is disconnected and the capacitor discharges through the resistors.
Seen from the capacitor terminals:

Left path:

Right path:

These two paths are in parallel:

Initial discharge current