Identify the mass number and atomic number from the given isotope notation.

The notation for an isotope is $^{A}_{Z}\text{X}$, where $A$ is the mass number (protons + neutrons) and $Z$ is the atomic number (protons).
For the uranium nucleus $^{238}_{92}\text{U}$:
Mass number ($A$) $= 238$
Atomic number ($Z$) $= 92$

The number of neutrons is found by subtracting the atomic number from the mass number.
Number of neutrons $= A - Z$
Number of neutrons $= 238 - 92$
Number of neutrons $= 146$

The calculated number of neutrons is 146, which corresponds to option B.

The number of neutrons in the nucleus of $^{238}_{92}\text{U}$ is $\boxed{\text{B) 146}}$.