[Edher]

What [OH-] should be maintained in a solution if, after precipitation of Mg+2 as
Mg(OH)2, the remaining Mg+2 is to be at a level of 1 microgram Mg2+ / L?
Ksp = 1.8x10^-11.

I found the initial concentration of OH- to be
After I did stoicheometry I foud that 1 microgram Mg2+ / L is tantamount to 4.11x10^-8 moles.

What exactly do I do with this result? Am I supposed to add it to the initial [OH-]
that's what I did and I didn't get the right answer. According to the book, the answer should be 0.02M.

Edher

[Borek]

You have the definition of Qsp:

Qsp = [Mg²⁺ ][OH^- ]²

You know what final concentration (M) of Mg²⁺ is to be.

Simply rearrange above definition and you will find what concentration of OH^- is necessary to keep Mg²⁺ concentration below given treshold.

[AWK]

After I did stoicheometry I foud that 1 microgram Mg2+ / L is tantamount to 4.11x10^-8 moles.

Should be 4.17x10^-8

Correction added later - this number is for rounded mass of Mg to 24 - this causes error of 1.3 %.
 Your result is correct!