If the 12V adapter voltage is actually somewhat higher than 12V then you may be able to wire four LEDs in series, with 2 banks of them. You need a resistor in series with each bank of series LEDs. For a nominal 20mA of current and a nominal LED voltage of 3.1V, the resistor value would be (Measured adapter voltage - 3.1 x 4) / .020.
If the adapter voltage is actually only 12V then you can only have 3 LEDs in series max. You would then have two banks of three LEDs in series, and one bank of two LEDs. You need a resistor in series with each bank. The resistor values are(12V - 3.1 x 3) / .020 = 135Ω for the 3 LEDs in series, and (12V - 3.1 x 2) / .020 = 290Ω for the two LEDs in series.