Để tìm giá trị của \( m \) sao cho hệ phương trình có nghiệm duy nhất thỏa mãn \( 3x - 2y = 2 \), ta thực hiện các bước sau:

1. Giải hệ phương trình ban đầu:
\[
\begin{cases}
2x - my = m \\
x + 4y = m + 2
\end{cases}
\]

2. Tìm nghiệm của hệ phương trình này.

3. Kiểm tra nghiệm này có thỏa mãn phương trình \( 3x - 2y = 2 \) hay không.

Bước 1: Giải hệ phương trình ban đầu.

Từ phương trình thứ hai, ta có:
\[
x = m + 2 - 4y
\]

Thay \( x \) vào phương trình thứ nhất:
\[
2(m + 2 - 4y) - my = m
\]
\[
2m + 4 - 8y - my = m
\]
\[
2m + 4 - 8y - my = m
\]
\[
m - 8y - my = -4
\]
\[
m(1 - y) - 8y = -4
\]
\[
m - my - 8y = -4
\]
\[
m - y(m + 8) = -4
\]
\[
y(m + 8) = m + 4
\]
\[
y = \frac{m + 4}{m + 8}
\]

Thay \( y \) vào phương trình \( x = m + 2 - 4y \):
\[
x = m + 2 - 4 \left( \frac{m + 4}{m + 8} \right)
\]
\[
x = m + 2 - \frac{4(m + 4)}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4(m + 4)}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]
\[
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\]
\[
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\]
\[
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\]
\[
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\]
\[
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\[
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\[
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\[
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\]
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\]
\[
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\]
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\]
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\]
\[
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\[
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\]
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\]
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\]
\[
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\]
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\[
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\]
\]
\[
x = m + 2 - \frac{4m + 16}{m + 8}
\]