Okay, let's tackle this problem step by step. So, we need to find Chris's current age based on the information given. Let me start by breaking down the problem into smaller parts and writing down the equations that represent each statement. 

First, the problem says that the average of Amy's, Ben's, and Chris's ages is 6. Since there are three people, the total sum of their ages would be 3 times 6, which is 18. So, if I let A represent Amy's age, B represent Ben's age, and C represent Chris's age, then the first equation is:

A + B + C = 18.

Next, the problem states that four years ago, Chris was the same age as Amy is now. If four years ago Chris's age was equal to Amy's current age, then Chris's age four years ago would be C - 4. And that's equal to Amy's current age, which is A. So that gives me the second equation:

C - 4 = A.

Then, the third piece of information is that in four years, Ben's age will be 3/5 of Amy's age at that time. So, in four years, Ben's age will be B + 4, and Amy's age will be A + 4. According to the problem, B + 4 is equal to (3/5) times (A + 4). So that's the third equation:

B + 4 = (3/5)(A + 4).

Now, I have three equations:

1. A + B + C = 18
2. C - 4 = A
3. B + 4 = (3/5)(A + 4)

I need to solve these equations to find the value of C, which is Chris's current age.

Starting with equation 2: C = A + 4. So Chris's age is four years more than Amy's current age. That seems straightforward. 

Now, let's substitute equation 2 into equation 1 to eliminate C. So equation 1 becomes:

A + B + (A + 4) = 18

Simplifying that:

2A + B + 4 = 18

Subtract 4 from both sides:

2A + B = 14

So equation 4 is 2A + B = 14.

Now, equation 3 is B + 4 = (3/5)(A + 4). Let's solve equation 3 for B. Multiply both sides by 5 to eliminate the fraction:

5(B + 4) = 3(A + 4)

Expanding both sides:

5B + 20 = 3A + 12

Subtract 12 from both sides:

5B + 8 = 3A

Then, rearrange to solve for B:

5B = 3A - 8

So B = (3A - 8)/5.

Now, substitute this expression for B into equation 4 (2A + B = 14):

2A + (3A - 8)/5 = 14

To eliminate the denominator, multiply every term by 5:

5*2A + 3A - 8 = 5*14

Which is:

10A + 3A - 8 = 70

Combine like terms:

13A - 8 = 70

Add 8 to both sides:

13A = 78

Divide both sides by 13:

A = 6.

So Amy is currently 6 years old.

Now, using equation 2, Chris's age is C = A + 4 = 6 + 4 = 10. So Chris is 10 years old now.

But let's check if this makes sense with the other equations. Let's find Ben's age. From equation 4: 2A + B = 14, since A is 6, then:

2*6 + B = 14

12 + B = 14

B = 14 - 12 = 2.

So Ben is 2 years old now. Let's verify with equation 3. In four years, Ben's age will be 2 + 4 = 6. Amy's age will be 6 + 4 = 10. 3/5 of 10 is 6, which matches. So that checks out.

Let's also check the first equation: A + B + C = 6 + 2 + 10 = 18, which is correct.

Therefore, all the equations are satisfied with these values. So Chris is 10 years old now.

But wait, let me just make sure I didn't make any calculation mistakes. Let's go through the steps again quickly.

From the average, total age is 18. Four years ago, Chris was Amy's current age, so Chris is Amy + 4. Then, Ben's age in four years is 3/5 of Amy's future age. Solving the equations step by step gives Amy as 6, Ben as 2, Chris as 10. All equations hold. Yep, that seems right.

So the answer should be 10.
</think>