I was practising some problems on hydride shift and got stuck in this particular question. I wanted to know if hydride shift would take place in this particular case and which carbon would get the positive charge. Will a hydrogen from left or right carbon would shift??
I strongly suspect that a hydride shift is not observed in this example.
The reason is that it seems much more likely that you will have an alkyl shift instead, accompanied by ring contraction and formation of a carbonyl. This is essentially a pinacol rearrangement.
EDIT: Adding more details per @OscarLanzi comment...
I would think that this is the expected product after proton transfer.
It looks like the pinacol arrangement of 4,8-decalindiol has been known for quite some time. Hückel, Danneel, Schwartz, Gercke, Ann. 1929, 474, 121. and Meiser. Chem. Ber. 1899, 32, 2055.