There is no direct connection from Castellammare di Stabia to Capri. However, you can take the taxi to Sorrento then take the ferry to Capri. Alternatively, you can take the subway to Sorrento, take the walk to Sorrento, then take the ferry to Capri.
From Castellammare di Stabia taxi to Sorrento then ferry to Capri. 52 min 42€. From Via Nocera subway to Sorrento, walk to Sorrento, then ferry to Capri. 1 h 24 min 18€.