To solve the problem, we first interpret "X varies YZ" as meaning that \( X \) is proportional to the product of \( Y \) and \( Z \). This can be expressed mathematically as:
\[ X = k \cdot Y \cdot Z \]
where \( k \) is a constant.
From the problem, we have the values when \( Y = 2 \), \( Z = 3 \), and \( X = 30 \):
\[ 30 = k \cdot 2 \cdot 3 \]
Calculating the right side:
\[ 30 = k \cdot 6 \]
Now, we can solve for \( k \):
\[ k = \frac{30}{6} = 5 \]
Next, we need to find \( X \) when \( Y = 4 \) and \( Z = 6 \):
\[ X = k \cdot Y \cdot Z = 5 \cdot 4 \cdot 6 \]
Calculating the right side:
\[ X = 5 \cdot 24 = 120 \]
Thus, when \( Y = 4 \) and \( Z = 6 \), \( X \) equals 120.