To determine the overall noise figure of the cascaded amplifier system, we need to calculate the equivalent noise figure for each stage and then combine them.

Given data:
- Power gain (G) of each stage = 10 dB
- Noise figure (NF) of each stage = 6 dB

Calculating the equivalent noise figure for each stage:
- The noise figure (NF) is given in decibels (dB), which represents the ratio of the signal-to-noise ratio (SNR) at the input to the SNR at the output.
- The noise factor (F) is the ratio of the output noise power to the input noise power.
- The noise figure (NF) and noise factor (F) are related as follows: NF = 10 * log10(F).

Using this relation, we can calculate the noise factor (F) for each stage:
- For the given noise figure (NF) of 6 dB:
NF = 10 * log10(F)
6 = 10 * log10(F)
F = 10^(6/10) = 3.981

Calculating the overall noise figure:
- The overall noise figure (NF_total) can be obtained by combining the noise factors (F) of each stage using the formula: NF_total = 10 * log10(F_total).
- Since the noise factors are cascaded, the overall noise factor is given by: F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2) + ...

For the given three-stage cascaded amplifier system:
- F_total = F1 + (F2-1)/G1 + (F3-1)/(G1*G2)
= 3.981 + (3.981-1)/10 + (3.981-1)/(10*10)
= 3.981 + 2.981/10 + 2.981/(10*10)
= 3.981 + 0.2981 + 0.02981
= 4.30891

Finally, we calculate the overall noise figure (NF_total):
- NF_total = 10 * log10(F_total)
= 10 * log10(4.30891)
≈ 4.33 dB

Therefore, the overall noise figure of the cascaded amplifier system is approximately 4.33 dB, which corresponds to option 'C'.