Answer the following question based on the information provided.

Liam deposited $x$ dollars in account A for three years at a rate of 12% p.a. simple interest, whereas Sophia deposited $(x+4000)$ dollars in account B for two years at 20% p.a. compound interest. Find the amount deposited by Sophia if the total interest accumulated from both accounts is 3360 dollars.

The correct answer is 6000.

Step 1: Understand the given details
Let Liam's initial deposit in Account A be $x$ dollars.
Liam's account conditions:
- Principal ($P_{\mathrm{A}}$) = $x$
- Time ($T_{\mathrm{A}}$) = 3 years
- Rate of interest ($R_{\mathrm{A}}$) = 12% per annum simple interest

Sophia's account conditions:
- Principal ($P_{\mathrm{B}}$) = $(x+4000)$ dollars
- Time ($T_{\mathrm{B}}$) = 2 years
- Rate of interest ($R_{\mathrm{B}}$) = 20% per annum compound interest

Total interest earned from both accounts combined = 3360 dollars.

Step 2: Calculate the Simple Interest from Account A
The formula for Simple Interest (SI) is:

$\mathrm{SI}=\frac{P\times R\times T}{100}$

Substituting the values for Account A:

${\mathrm{SI}}_{\mathrm{A}}=\frac{x\times 12\times 3}{100}=\frac{36x}{100}=0.36x$

Step 3: Calculate the Compound Interest from Account B
The formula for Compound Interest (CI) over 2 years is:

$\mathrm{CI}=P\times \left[{\left(1+\frac{R}{100}\right)}^T-1\right]$

Substituting the values for Account B:

${\mathrm{CI}}_{\mathrm{B}}=(x+4000)\times \left[{\left(1+\frac{20}{100}\right)}^2-1\right]$

${\mathrm{CI}}_{\mathrm{B}}=(x+4000)\times \left[{\left(1.2\right)}^2-1\right]$

${\mathrm{CI}}_{\mathrm{B}}=(x+4000)\times (1.44-1)$

${\mathrm{CI}}_{\mathrm{B}}=0.44\times (x+4000)=0.44x+1760$

Step 4: Form the total interest equation and solve for $x$
Total Interest = ${\mathrm{SI}}_{\mathrm{A}}+{\mathrm{CI}}_{\mathrm{B}}$

$0.36x+0.44x+1760=3360$

$0.80x+1760=3360$

$0.80x=3360-1760$

$0.80x=1600$

$x=\frac{1600}{0.80}=2000$

Step 5: Find the amount deposited by Sophia
The amount deposited by Sophia is $(x+4000)$ dollars.

$\text{Sophia's deposit}=2000+4000=6000$

Thus, the amount deposited by Sophia is 6000 dollars.