Hexadecimal seven segment display verilog

You are not using enough voltage.
The page you referenced notes that there multiple LEDs in series.
They say:

• Large (58mm) 7-segment LED display
  Digits color can be either red or green.
  Type: 12101BEG
  If max: 30mA
  If peak 1/10 dutycycle, 0.1ms: 100mA
  Vf red: 7.2-8.8V
  Vf green: 8.8-10.0V
  Each segment consists of four LEDs connected in series.

In most cases simply trying every combination in turn will work.
There is a small chance that you will destroy segment LEDs with reverse voltage.

Supply two leads from psu via a resistor so you can easily swap both leads.
Try each combination in turn.
A1 A2 A3 A4 A5 B1 B2 .......

The red wire is hooked up to the 5v output on the arduino and the blue to the ground. As can be seen the decimal point has been lit up in green, and if I move the red wire four pins to the left the decimal point turns red instead.

As they say CA = common Anode = common +ve you may have
2 x Anode's
+ 8 x Cathodes.
So Bottom right may be common green anode and
bottom left = common red anode.

SO increase Vsupply to say 8V, use a 10k resistor for initial safety, put V+ on bottom right and try all pins with v-. If that works then put V+ via 10l on bottom left and repeat.

The supplier should be able to provide a datasheet.

Your code there doesn't look generally synthesizeable to me, as you're not really following any synchronous design conventions. I expect if you inspect your synthesis logs you'll find several warnings and/or errors.

1. An edge triggered always block should model a flip flop, which means that it has one edge triggered clock, and an optional edge triggered preset and/or reset. It should not be triggering on edge of multiple arbitrary signals. @(posedge clk or negedge en) would be more appropriate, assuming that your fpga is provided with a suitable clock signal.

2. Inside of an edge triggered block, you should generally use non-blocking assignments: <=, instead of blocking assignments: =, as this more correctly models the behavior of a flip flop. If you don't know what this means then do some research between the difference between blocking and nonblocking assignments.

If you want to use memory elements like a counter, then you need to use clocked logic. On every clock edge you can check if in_up or in_down has changed from the previous value, and then use that to decide if you want to increment or decrement your counter value. You may need to debounce the input signals if they are coming from a button or you may get multiple spurious toggles when it's pressed.