Let's define the unknown number as $x$.

According to the problem, the cube root of the number, increased by four, equals six. We can write this as the equation:

$\sqrt[3]{x} + 4 = 6$

To solve for $x$, follow these steps:

1. Subtract 4 from both sides:

$\sqrt[3]{x} = 6 - 4$ $\sqrt[3]{x} = 2$

2. Now, cube both sides to eliminate the cube root:

$x = 2^3$ $x = 8$

So, the number is $x = 8$.

Would you like further details or explanations?

Here are five related questions to expand your understanding:

1. What is the cube root of $27$ plus 3?
2. If the cube root of a number increased by 5 is 10, what is the number?
3. How would you solve the equation $\sqrt[3]{x + 2} = 4$?
4. Can you find the cube of a negative number, for example, $(-3)^3$?
5. How do cube roots differ from square roots in terms of solving equations?

Tip: When solving equations involving cube roots, remember that the cube root of a negative number is negative!