To solve the given optimization problem using Gurobi, we need to first define the variables and the objective function. Then, we'll add the constraints as specified in the problem description.

The objective is to minimize \(3x_0 + 6x_1\), where \(x_0\) represents the milligrams of vitamin K and \(x_1\) represents the milligrams of vitamin B6.

Given constraints:
- The digestive support index for vitamin K is 9, and for vitamin B6 is 8.
- The energy stability index for vitamin K is 9, and for vitamin B6 is 20.
- The cognitive performance index for vitamin K is 11, and for vitamin B6 is 17.
- Combined indices have specific minimum and maximum bounds.

Let's define the variables and constraints in Python using Gurobi:

```python
from gurobipy import *

# Create a model
m = Model("Optimization_Problem")

# Define the variables
x0 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_K")
x1 = m.addVar(vtype=GRB.CONTINUOUS, name="milligrams_of_vitamin_B6")

# Objective function: Minimize 3*x0 + 6*x1
m.setObjective(3*x0 + 6*x1, GRB.MINIMIZE)

# Constraints:
# Digestive support index constraints
m.addConstr(9*x0 + 8*x1 >= 28, name="digestive_support_min")
m.addConstr(9*x0 + 8*x1 <= 57, name="digestive_support_max")

# Energy stability index constraints
m.addConstr(9*x0 + 20*x1 >= 13, name="energy_stability_min")
m.addConstr(9*x0 + 20*x1 <= 49, name="energy_stability_max")

# Cognitive performance index constraints
m.addConstr(11*x0 + 17*x1 >= 29, name="cognitive_performance_min")
m.addConstr(11*x0 + 17*x1 <= 59, name="cognitive_performance_max")

# Additional constraint
m.addConstr(-7*x0 + 9*x1 >= 0, name="additional_constraint")

# Optimize the model
m.optimize()

# Print the solution
if m.status == GRB.OPTIMAL:
    print("Optimal solution found:")
    print(f"Milligrams of vitamin K: {x0.x}")
    print(f"Milligrams of vitamin B6: {x1.x}")
else:
    print("No optimal solution found.")
```

This code defines the problem as specified, with the variables representing milligrams of vitamins K and B6, the objective function to minimize, and all given constraints. It then solves the optimization problem using Gurobi's `optimize` method and prints out the result if an optimal solution is found.