What is the trick behind this math?

Can somebody help me on how they use mathematics to arrive at this answer.
2 + 12 + 8 = 13
What is happening here.?

I hope you’re trolling…

Or perhaps you wrote a wrong mathematical expression instead of you might have wanted to write otherwise?

where did you find it? that could help explaining what’s going on, if it is just wrong or if there is something else

I burst into Luhn’s Algorithm for validatiion of number and I was lost at the point I encounter this line

Now that you have given some context (Luhn’s Algorithm for validatiion of number), the 12 becomes 1 + 2 which is equal to 3, so really it is 2 + 3 + 8 which is equal to 13.

I understand, but am the type that always want to know how things got cooked up. My worry is how do they come about splitting 12 into 1 and 2, are they coming from hexdecimal perspective or which part of math do they get the logic from ?

It is just part of the algorithm. To understand more than that, you would need to dive deep into the mathematics behind it.

Do you have any clue on what to study or relevant material that help hasten me journey into it?

I would start here and then look at any cited or linked references. After that, you can use Google to search for more specific math theory related to the information presented.