I learnt a second language from scratch as an adult. The neural plasticity thing is definitely real but I think the effect is often overstated. Adults a) rarely spend as much focused time on language study as kids and b) are more afraid of making mistakes/less inclined to say things that they know are not 100% right. I've observed that people who care less about making mistakes (to the point where it's embarrassing to watch) end up learning much faster.