Karatsuba Multiplication Rule in dividing a Number in two parts
The most common approach is to take the longest number, and divide it in half (rounding an odd number of digits arbitrarily). So for

x = 12345
y = 2478


you would get a=12, b=345, c=2, d=478. Since the number of digits in x is not even, we are free to choose whether to split into a=12 and b=345 or a=123 and b=45; it makes no difference to the running time. For your second example

x = 12456778
y = 241


you would get a=1245, b=6778, c=0, d=241.