**Solution:**

Given,
- Principal amount (P) = 4000
- Interest rate (R) = 6%
- Amount (A) = 5353

Let's use the formula for compound interest to find the number of years:

A = P(1 + R/100)^n

where n is the number of years.

**Step 1:** Calculate the interest rate in decimal form

R = 6/100 = 0.06

**Step 2:** Rewrite the formula with the given values

5353 = 4000(1 + 0.06)^n

**Step 3:** Solve for n

Dividing both sides by 4000, we get:

1.33825 = (1 + 0.06)^n

Taking the logarithm of both sides with base 10, we get:

log 1.33825 = n log (1 + 0.06)

n = log 1.33825 / log 1.06

n = 4 years (approx.)

Therefore, the sum was invested for 4 years.

**Explanation:**

Compound interest is the interest earned on both the principal amount and the interest earned in previous years. In this problem, we are given the principal amount, the interest rate, and the final amount. We need to find the number of years for which the sum was invested.

To solve this problem, we can use the formula for compound interest, which relates the principal amount, interest rate, number of years and the final amount. We can rearrange this formula to find the number of years given the other values.

In this case, we first calculated the interest rate in decimal form by dividing the given rate by 100. We then substituted the given values into the formula and solved for n by taking logarithms of both sides.

The final answer is that the sum was invested for 4 years.