Zipper multiplication
Jelly, 11 10 bytes

ƓDUz0P€Uḅ³


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I couldn't get this down to 10 bytes by myself, but @Pietu1998 pointed me to an atom I'd missed, this giving this 10-byte solution. Unusually for Jelly, this one takes input from standard input (in the form 1276,933024), not from the command line (this enables the use of the ³ command, which returns the command line argument, defaulting to 100).

Explanation:

ƓDUz0P€Uḅ³
Ɠ           read standard input
 D          convert to base 10
  U         reverse elements
   z0       transpose, padding the end with zeroes
     P€     take the product of each (€) inner list
       U    reverse elements back
        b³  convert from base 100


The use of base 100 is a simple way to implement the "pad to 2 digits, then convert to base 10" technique. The only other subtle thing here is the reversing; we want to pad with zeroes at the start of the number, but Jelly's z command pads at the end, so reversing the lists means that z will pad correctly.