Thorium-234 undergoes beta decay to form a daughter nuclide and a beta particle. what are the mass number and atomic number for the daughter nuclide?

Radioactive decay in this case is the beta decay. Where Thorium will give out a beta particle and decay into the daughter nuclide. 
Beta particles are β⁻, a neutron in the nucleus is converted to a proton and an electron is released. Beta particles are therefore negatively charged and have no mass.
from the parent nuclide to daughter nuclide, there is no change in mass number , however in the parent a neutron converted to proton so there's an additional proton, this means that atomic number also increases by 1. then the daughter nuclide is the element with the corresponding atomic number 

²³⁴₉₀Th > ²³⁴₉₁Pa + ₋₁⁰β

Th atomic number - 90 , after beta decay proton increases by 1, atomic number of daughter nuclide is 91, the element with atomic number 91 is protactinium.
As neutron converts to proton no net change in mass.