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**Hint:**According to the Bohr's model in the atoms the electrons are moving around the nucleus in different shells. These shells are K, L, M, N etc. Electronic distribution of an atom/ion is an arrangement in a space of the electrons around the center of the mass(nucleus) of the atom or ion among the orbits or shells.

**Complete step by step answer:**

The principle quantum numbers of the shells are, for K is 1, for L is 2, for M is 3, for N is 4 etc.

According to the principal quantum number the total electrons can be filled in a shell is \[2{n^2}\].

Therefore, the total electrons in K shell is 2, in L shell is 8, in M shell is 18 and so on.

Therefore, the electron distribution of \[{M^{ + 2}}\] is

K | L | M |

2 | 8 | 14 |

Now the number of electrons of an element is equal to the number of protons.

Therefore, the total number of protons present in \[{M^{ + 2}}\] is 24.

Now the atomic weight of \[{M^{ + 2}}\] is equal to 58.

\[atomic{\text{ }}weight = {\text{ }}proton{\text{ }}number{\text{ }} + {\text{ }}neutron{\text{ }}number{\text{ }}\]

Therefore, the number of neutrons is

\[

atomic{\text{ }}weight = {\text{ }}proton{\text{ }}number{\text{ }} + {\text{ }}neutron{\text{ }}number{\text{ }} \\

or,58 = 24 + neutron{\text{ }}number{\text{ }} \\

or,neutron{\text{ }}number{\text{ }} = 58 - 24 \\

or,neutron{\text{ }}number{\text{ }} = 34 \\

\]

**Therefore, the correct option is C.**

**Note:**Remember that atomic weight is equal to the summation of proton and neutron. Also remember that in an atom the total number of electrons in the shells is equal to the number of protons in the nucleus. The principal quantum number for different shells are,1 for K, 2 for L,3 for M, 4 for N etc.

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