The magnetic field generated by a wire carrying a current I is:
[tex]B(r) = \frac{\mu_0 I}{2 \pi r} [/tex]
where r is the distance at which the magnetic field is measured, and [tex]\mu_0 = 4 \pi \cdot 10^{-7} NA^{-2}[/tex] is the magnetic permeability in vacuum.
The problem says that the magnetic field at a distance r=12 cm=0.12 m from the wire must be no larger than [tex]B=0.5 \cdot 10^{-4}T[/tex]. Substituting these values, we can find the maximum value of the current I that the wire can carry:
[tex]I= \frac{2 \pi r B}{\mu _0} = \frac{2 \pi (0.12 m)(0.5 \cdot 10^{-4}T)}{ 4 \pi \cdot 10^{-7} NA^{-2}}= 30 A[/tex]
