The molecular mass of ${\left(N{H}_4\right)}_{2}C{O}_3$ is: Given atomic mass of H =1, O =16, C = 12, N = 14. 

Atoms each have a distinct atomic mass that is determined empirically. Similar to this, the atomic masses of the atoms that make up a given molecule are used to calculate the molecule's molecular mass.

For a better understanding, first provide us some detailed information on the atomic and molecular masses.
Atomic mass is only the weight of an atom found in the current periodic table. The kilogramme is its SI unit.
A given molecule's mass, which is made up of multiple atoms, is known as its molecular mass. Calculations using stoichiometry can employ either molecular mass or molar mass, or vice versa.
In actuality, it is computed by adding the atomic weights of the atoms that make up a substance's molecular formula.
For example, in order to calculate the molecular mass of any material, we must first determine the atomic masses of the individual atoms that make up the substance.

Molecular mass or molar mass of a compound is the sum of mass of all the atoms present. Given the formula of ammonium carbonate;${\left(N{H}_4\right)}_{2}C{O}_3$.
By summing up the mass of all atoms we can calculate its molar mass.

${\left(N{H}_4\right)}_{2}C{O}_3\equiv {\mathrm{N}}_2{\mathrm{H}}_8{\mathrm{CO}}_3$

Given atomic masses ;H=1 g

O=16 g

C=12 g

N=14 g

$molar mass=(2\times 14)+(8\times 1)+(1\times 12)+(3\times 16)$

$\Rightarrow 28+8+12+48=96 \mathrm{g}$

Correct answer is 96 g/mol.