Answer
$B = 0.252~T$
Work Step by Step
The magnetic field is directed out of the page.
When the particle first enters the magnetic field, the force on the particle is to the left.
Therefore, by the right hand rule, the particle must have a positive charge.
Then the particle must be a proton.
Note that $\frac{T}{2} = 130~ns$
We can use the equation for the period to find the magnitude of $B$:
$T = \frac{2\pi~m}{q~B}$
$B = \frac{2\pi~m}{q~T}$
$B = \frac{(2\pi)~(1.67\times 10^{-27}~kg)}{(1.6\times 10^{-19}~C)(260\times 10^{-9}~s)}$
$B = 0.252~T$
