Resistor Placement

Wiring 4 LEDs in series, and driving from a single Arduino pin could be a problem. The 3.3 or 5 volts from the Arduino might not be enough, since each LED needs a minimal voltage drop across it before it lights. That varies depending on the color of the LED, but figure 2 volts as a ball park. That would need at least 8 volts to light them up.

Instead, still using only a single Arduino pin, wire each LED in series with the appropriate current limiting resistor. Then wire all 4 sets (LED + resistor) in parallel to the single Arduino Pin. As long as the total current needed by the 4 LEDs does not max out the drive limit of the Arduino pin, that will work fine.

      |—— led —— resistor —— ground
      |
      |—— led —— resistor —— ground
pin ——|
      |—— led —— resistor —— ground
      |
      |—— led —— resistor —— ground

Edit: vanepp solution also works, and will use about half the current. As long as the Arduino pin can drive a high enough voltage to get both LEDs to light. 3.3V is likely not enough. 5V is. In each of these cases, the correct currently limiting resistor will be different: Supply voltage minus sum of LED voltage drops (at desired current) give the correct voltage drop across the resistor. That voltage and current determine the resistor value.

Edit2: the voltage and current values coming from each parallel path. For all 4 in seres, 4 x LED voltage drop; for vanepp solution 2 x LED voltage drop; for mine, 1 x LED voltage drop;