If $y$ varies directly with $x$, we can write the relationship as:

$y = kx$

where $k$ is the constant of proportionality.

Step 1: Find the constant $k$

When $y = 6$ and $x = 2$: $6 = k \cdot 2$ $k = \frac{6}{2} = 3$

Step 2: Use $k$ to find $y$ when $x = 12$

Substitute $k = 3$ and $x = 12$ into the equation: $y = 3 \cdot 12 = 36$

Final Answer:

The value of $y$ when $x = 12$ is 36.

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Would you like a detailed explanation or have any questions? Here are some related questions for practice:

1. If $y$ varies directly with $x$, and $y = 10$ when $x = 5$, what is $y$ when $x = 20$?
2. What is the equation of direct variation if $y = 8$ when $x = 4$?
3. If $y = kx$ and $k = 7$, what is $y$ when $x = 9$?
4. How would the graph of $y = kx$ look if $k = -2$?
5. If $y$ varies directly with $x$, and $y = 15$ when $x = 3$, what is $x$ when $y = 45$?

Tip: Always isolate the constant of proportionality $k$ first in direct variation problems!