Dell's buyout of EMC in 2015
HP's buyout of Compaq in 2002
Google's buyout of Motorola in 2011
Microsoft's buyout of LinkedIn in 2016
 
Correct Answer: Dell's buyout of EMC in 2015

A little background…

It may not be the most recognizable deal, but Dell's acquisition of enterprise storage company EMC for $67 billion in cash and stock stands as the tech industry's largest buyout. Second place goes to Microsoft's purchase of LinkedIn for $26.2 billion in 2016.

HP's takeover of Compaq in 2002 is virtually tied with Facebook's buyout of WhatsApp for third with both being ~$19 billion exchanges (the HP-Compaq deal is often cited as being $25-$33 billion but it fell to $18.6 billion in the end). HP's $15.4 billion acquisition of Ross Perot's IT services company EDS in 2008 is also notable, and for completion's sake, Google paid $12.5 billion for Motorola and sold it to Lenovo two years later for $2.9 billion (minus all the patents).

You may be wondering why AOL's buyout of Time Warner isn't among the answers, considering it was a larger deal than any of those, with AOL paying $106 billion for Time Warner in 2000 (it was actually originally $165 billion but later reduced). However, that acquisition is typically excluded from this sort of list because AOL and Time Warner are considered media companies more than tech companies.