IUPAC name of complex {{K}_{3}}[Al{{({{C}_{2}}{{O}_{4}})}_{3}}] (a)- Potassium aluminum-oxalate(b)- Potassium trioxalatoaluminate(III)(c)- Potassium aluminium(III) oxalate(d)- Potassium trioxalatoaluminate(VI)

The complex is \[K_3[Al(C_2O_4)_3]\]. Let's break it down step-by-step to find its IUPAC name:

### 1. **Identify the cation and anion:**
- The cation here is \( K^+ \) (Potassium).
- The anion is the complex ion \([Al(C_2O_4)_3]^{3-}\).

### 2. **Oxalate ligand**:
- \( C_2O_4^{2-} \) is the oxalate ion. In coordination chemistry, it is referred to as "oxalato."

### 3. **Aluminum as the central metal**:
- The central metal is aluminum (Al), which is in the anionic complex. When naming an anionic complex, the suffix “-ate” is added to the name of the metal.
- Therefore, aluminum becomes **"aluminate"** in the name.

### 4. **Oxidation state of aluminum**:
- To determine the oxidation state of aluminum, consider that each oxalate ligand \( C_2O_4^{2-} \) has a charge of \( -2 \), and there are three oxalate ions, so the total negative charge from the oxalate ligands is \( -6 \).
- Since the overall charge of the complex ion is \( -3 \), and we know that the sum of the charges in the complex must equal the charge of the complex ion, the oxidation state of aluminum (Al) must be \( +3 \).

### 5. **Putting it all together**:
- There are 3 potassium ions to balance the \( -3 \) charge of the complex ion \([Al(C_2O_4)_3]^{3-}\).
- The IUPAC name of the complex is based on the ligands (oxalate), the central metal (aluminum), and its oxidation state (III).

Thus, the IUPAC name of \[K_3[Al(C_2O_4)_3]\] is:

**Potassium trioxalatoaluminate(III)**.

### Answer:
(b) Potassium trioxalatoaluminate(III)