"How many engineers do you know?"
Translation:Sen kaç tane mühendis tanıyorsun?
"tanımak" is only for knowing people. bilmek is "to know something" in general.
you might use bilmek with people only in some contexts. e.g. you can say "Duolingo'daki Selcen'i biliyorum" (I know Selcen from Duolingo) because you have heard about me, but you don't actually know me (that would be "Duolingo'daki Selcen'i tanıyorum")
Tanımak and hatırlamak can sometimes be interchangeable, but sometimes not. Tanımak (to recognize) is actually about indentifying something with your five senses (usually seeing though). So it might be more suitable or less suitable to use it in certain situations.
Bu kitabı tanıdın mı? Senin kitabın! (Do you recognize this book? It's yours!)
Bu kitabı hatırladın mı? Bana önermiştin. (Do you recognize/remember this book? You had recommended it to me.)
As you see there is a slight difference in the meaning. The latter is not supposed to be the same book physically.
You are right about 'tanıyorum'. It's not wrong but we don't tend to use it in present tense. You should say Bu kitabı tanıdım. (I have recognized this book.)
Especially in some cases hatırlamak can't be used instead of tanımak.
Onun yazısını tanıdım. - I recognized his writing.
Filistin'i tanıdılar. - They recognized Palestine.
Sorry but I don't agree with you. It sounds perfect to me! :D I think Turkish speakers also have the right to distinguish between to recognise and to remember as English speakers do, we just deserve it. TDK already recognizes this right.
I am serious maybe it's me but it doesn't sound clumsy to me. I expect other native speakers to comment on it.
Accusative case is only for specific /definite direct objects, and here we are asking about general /indefinite /unspecific engineers. In this sentence, they aren't THE engineers, THOSE engineers, MY engineers, etc. (specific), but they are some unspecified engineers from no particular group or place (general). :-)