It's easy. If ants grew to the size as in the picture, there are really only four possibilities:

• they would be direct threat to humans, meaning they would become extinct very quickly
• they would attack our livestock and crops, meaning they would either become extinct or decimated and driven out of human infested areas into deep woods
• as hunter-gatherers they would directly compete with humans for wildlife meaning extinction or decimation
• in a rare possibility that they were somehow useful to humans they could proliferate (although changed); f.e. if they could be controlled in some reliable way they could be used in warfare; if they were collecting or growing something that humans want (like bees producing honey) they would be domesticated or - if domestication was not an option - their nests would be raided for bounty (but like with all useful wildlife sooner or later they would be protected to preserve enough for us to exploit)

In any of the above scenarios their fate would be bleak.