I can't remember the exact figures, but according to him the Soviet Union had between 20,000-30,000 tanks (I will edit if someone can point out the exact figures in his claim).
I am not sure that all references count the exact same type of vehicle (tank is loosly defined). But they are all in the same area of about 20000 tanks.
According to Wikipedia
The Soviet Union began and ended the war with more tanks than the rest of the world combined (18,000-22,000)
Another article cites numbers of over 25000
Figures are up until the first half of 1945 and only include new production. The Soviet Union had 25,664 or 25,481 armoured fighting vehicles on 1 June 1941 before it entered the war.
Wikipedia references the second number with a website in Russian (google translate)
A much lower number is mentioned in the article about Operation Barbarossa
Tanks (incl assault guns) 15,687
However operationbarbarossa.net says
As a case in point let us examine the Red Army’s tank park in June 1941. On 22nd June 1941 the Soviets had 23 295 tanks in service (including non-operational tanks in various states of repair in rear areas).
of the rather incredible 20 500 tanks lost by the Soviets in 1941, the large majority were destroyed by PaK 36s
That means to loose that many tanks you have to have these in the first place.
They list references at the bottom, but i have not been able to verify those.
(5) T. Bean, W. Fowler, Russian Tanks of WWII-Stalin’s Armoured Might, Ian Allan Publishing, London, 2002, appendix, p170. Also, S. J. Zaloga, L.S. Ness, Red Army Handbook 1939-1945, Sutton Publishing, Stroud, UK, 1998, p. 181, table 6.3. 20 500 Soviet tanks lost vs. 2 758 German tanks lost in 1941.