A certain weak base has a Kb of 8.40 × 10-7. What concentration of this base will produce a pH of 10.34?

Didn't I do this for you a couple of days ago? I think so.

pH = 10.34; pOH = 3.66; (OH^-) = about, but an estimate = 2E-4

........BOH ==>B^+ + OH^-
I.......x......0......0
C........-y....y.......y
E.......x-y....y......y

y = 2E-4 from above.
Kb -= (B^+)(OH^-)/BOH)
Substitute into Kb expression and solve for x. Post your work if you get stuck.