Write the complex clearly

The compound is: $[Pt(NH_3)_2Cl(NH_2CH_3)]Cl$

This contains:

• Complex cation: $[Pt(NH_3)_2Cl(NH_2CH_3)]^+$
• Counter anion: $Cl^-$

Identify the ligands inside the coordination sphere

Inside the bracket, the ligands are:

• $2$ molecules of $NH_3$ = ammine
• $1$ ligand $Cl^-$ = chlorido
• $1$ ligand $NH_2CH_3$ = methylamine, IUPAC ligand name = methanamine

Find the oxidation state of Pt

Let oxidation state of Pt be $x$.

In the complex:

• $NH_3$ is neutral
• $NH_2CH_3$ is neutral
• $Cl^-$ is $-1$
• Overall charge on complex ion is $+1$

So, $x + 0 + 0 - 1 = +1$ $x = +2$

Hence, the metal is platinum(II).

Arrange ligand names in alphabetical order

Ligands are named alphabetically, ignoring multiplicative prefixes like di-, tri-, etc.

Ligand names:

• ammine
• chlorido
• methanamine

Alphabetical order:

• ammine
• chlorido
• methanamine

Since there are two ammine ligands, it becomes diammine.

Name the cation and then the anion

So the complex cation is named: $\text{diamminechlorido(methanamine)platinum(II)}$

Since there is one chloride ion outside the coordination sphere, the full name becomes: $\text{diamminechlorido(methanamine)platinum(II) chloride}$

Check options

• A: Diamminechlorido (methanamine) platinum(II)chloride. ✅ Correct in substance.
• B: Biasmmine (methanamine)chlorido platinum(II)chloride. ❌ Wrong prefix/spelling/order.
• C: Diamminechlorido (amminomethane) platinum(II) chloride. ❌ Wrong ligand name.
• D: Diammine (methanamine) chlorido platinum(II)Chloride. ❌ Ligand order incorrect.

Final answer

The correct IUPAC name is: $\boxed{\text{Diamminechlorido(methanamine)platinum(II) chloride}}$

Hence, Option A is correct.