Answer:
Six German Battleships were sunk in WW II, by German definitions, although only two were widely considered as true modern battleships.
Bismarck and her sister, Tirpitz were splendidly armored, and armed modern battleships. Germany did consider Scharnhorst and Gneisenau battleships too, but these two ships were widely considered battlecruisers by other countries, although in no way did they resemble battlecruisers except in speed (they were very heavily armored, and lightly gunned, battlecruisers were not generally well armored).
Germany also lost two very old pre-Dreadnought battleships, Schleswig-Holstein and Schlesien. These ships were not much larger than a heavy cruiser, however, and in no way resembled a battleship of that period.
The so called "Pocket Battleships" were not considered battleships by any navy, despite their name. Germans considered them "armored cruisers", and in any event, they were smaller and displaced less than German heavy cruisers from that time.
The correct answer is six, going by what the Germans considered the units, but it could be four if you only consider modern ships, or two if you only consider what were internationally accept as true battleships.