A question on diodes and resistors at the OR gate inputs of a 7432 IC
What could be the reasons for the diodes and the resistors in the inputs of the OR gates of the 74LS32?


They prevent damage to the chip if the input signals go negative. The diodes provide an alternate path for current to flow when that happens, and the resistors limit the current that can flow.


  Can this 74LS32 handle 6V or 12V voltage inputs at its OR gates?


No. Generally an input voltage higher than the positive supply voltage of a logic gate has the potential to damage the chip.

In newer chips this restriction would be given in an "Absolute Maximum Ratings" table. For these very very old chips, probably this table was once found in a general information about the whole LS family at the front of the databook, and On Semi just hasn't gotten around to including it in every individual datasheet in the years since things went online and those general information sections from the databook got hard to find.