Step 1: Recall Bohr's idea.
In Bohr's model, electrons can only orbit in certain allowed paths. In these paths the angular momentum takes only special values.
Step 2: Write the quantization rule.
The angular momentum of the electron is a whole-number multiple of $\dfrac{h}{2\pi}$. \[ L = n\frac{h}{2\pi} \] where $n = 1, 2, 3, \dots$ and $h$ is Planck's constant.
Step 3: Identify the basic unit.
The smallest step, when $n = 1$, is \[ L = \frac{h}{2\pi} \] This is the basic packet of angular momentum.
Step 4: Connect to the orbit.
The angular momentum is also $L = mvr$, the mass times speed times radius. Setting this equal to $n\dfrac{h}{2\pi}$ gives the allowed orbits.
Step 5: Rule out the others.
Choices like $h$, $2\pi/h$, or $h/\pi$ do not match the correct unit of $h/2\pi$.
Step 6: State the answer.
The angular momentum is an integer multiple of $h/2\pi$. \[ \boxed{L = n\frac{h}{2\pi}} \]