most toyota model numbers will follow this pattern
example: 42-6FGCU20-10447
This can be found on the dataplate located on the front cowl
(in your case we can assume the truck has been painted and the dataplate has been removed or fell off at some point in the machines life)
The serial number will still be stamped into the frame somewhere on top or side of the frame usually around the hood area or front along the foot step area or possibly on the front of the cowl.
(sometimes if truck has been painted some scraping has to be done to find it)

first 2 numbers determine engine type and transmission

4 designates a 4Y engine
2 designates a powershift transmission

next sequence of numbers/letters

6 designates the model changes or design series
F designates type of machine F being forklift
G designates type of power G being Gasoline/LP
C designates types of tires C being cushion (in your case there would be no letter Pneumatic is left blank)
U designates mfg country U being united states, if blank that designates Japan
20 designates capacity (20 equal to 2000k or 4409lbs)

the last group of numbers following would be the truck serial number.

without the serial number there is no way of tracking down the actual model number but from looking at the picture we can figure at least it is an FG20 , 23 or 25.
If you want to order parts for this unit you will need the complete model number though. If it is a japan built truck (grey market truck) that will make a difference in getting parts also.