To simplify the expression \((2x + y)^3 - 2(y - x)^3\), we need to expand each term separately and then combine like terms. Let's start with the expansion.

### Step 1: Expand \((2x + y)^3\)
Using the binomial theorem, \((a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3\), we get:
\[
(2x + y)^3 = (2x)^3 + 3(2x)^2(y) + 3(2x)(y^2) + y^3
\]
\[
= 8x^3 + 3 \cdot 4x^2 \cdot y + 3 \cdot 2x \cdot y^2 + y^3
\]
\[
= 8x^3 + 12x^2y + 6xy^2 + y^3
\]

### Step 2: Expand \((y - x)^3\)
Using the binomial theorem again, \((a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3\), we get:
\[
(y - x)^3 = y^3 - 3y^2(x) + 3y(x^2) - x^3
\]
\[
= y^3 - 3y^2x + 3yx^2 - x^3
\]

### Step 3: Multiply \((y - x)^3\) by \(-2\)
\[
-2(y - x)^3 = -2(y^3 - 3y^2x + 3yx^2 - x^3)
\]
\[
= -2y^3 + 6y^2x - 6yx^2 + 2x^3
\]

### Step 4: Combine the expanded terms
Now, we combine the expanded forms of \((2x + y)^3\) and \(-2(y - x)^3\):
\[
(2x + y)^3 - 2(y - x)^3 = (8x^3 + 12x^2y + 6xy^2 + y^3) + (-2y^3 + 6y^2x - 6yx^2 + 2x^3)
\]

Combine like terms:
\[
= 8x^3 + 2x^3 + 12x^2y - 6x^2y + 6xy^2 + 6xy^2 + y^3 - 2y^3
\]
\[
= 10x^3 + 6x^2y + 12xy^2 - y^3
\]

So, the simplified form of the expression \((2x + y)^3 - 2(y - x)^3\) is:
\[
10x^3 + 6x^2y + 12xy^2 - y^3
\]