Good job! Here's the reason that the LED's need their own resistors (If you want them all to be the same brightness - you actually need one resistor per LED)
Different coloured LED's have different forward voltage drops. for example a red LED might have a forward voltage drop of 2v whereas green or blue might be 2.5v
If you don't give an LED it's forward voltage drop - it won't turn on. Also, because an LED is a diode - once it has reached it's forward voltage drop - it will not drop any more voltage.
So if you have a red and green LED in parallel - only the red one will turn on because the red one will be fixed at 2v whereas the green one cannot turn on because it needs 2.5v
Connecting them like this will make sure that all LED's will turn on. Also, notice how the resistor in series with the LED's can have a different voltage drop (due to the LED's forward voltage drop) if you want them to have the same amount of current, you need to select different values of resistance to give them the required current.

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for example let's say the RED led had a forward voltage drop of 2v, which leaves 10v for the resistor. if we want 20mA flowing through this LED then 10v / 20mA = 500 ohms. Now to make the green LED have the same current we need to apply the same principle:
2.5v on the LED, therefor 9.5v on the resistor so: 9.5v / 20mA = 475 ohms.
Hope that helps!