To solve the equation \( 44:(2x + 1) = 4 \), follow these steps:

1. **Rewrite the equation**:
\[
\frac{44}{2x + 1} = 4
\]

2. **Eliminate the fraction** by multiplying both sides of the equation by \( 2x + 1 \):
\[
44 = 4(2x + 1)
\]

3. **Distribute** the 4 on the right-hand side:
\[
44 = 8x + 4
\]

4. **Isolate the term with \( x \)** by subtracting 4 from both sides:
\[
44 - 4 = 8x
\]
\[
40 = 8x
\]

5. **Solve for \( x \)** by dividing both sides by 8:
\[
x = \frac{40}{8}
\]
\[
x = 5
\]

So, the solution to the equation \( 44:(2x + 1) = 4 \) is \( x = 5 \).