**Solving the Equation:**

To solve the equation, we need to simplify and isolate the variable y. Let's break down the given equation step by step:

The equation is: \(\frac{{-2}}{{5y - 3}} = -\frac{{1}}{{4}}\)

**Step 1:**
To start, let's cross-multiply the equation to eliminate the fractions:

\(-2 \times 4 = -1 \times (5y - 3)\)

Simplifying, we get:

\(-8 = -5y + 3\)

**Step 2:**
Next, we can rearrange the equation by moving the constant term to the other side:

\(-5y = -8 - 3\)

Simplifying the right side:

\(-5y = -11\)

**Step 3:**
Now, we can solve for y by dividing both sides of the equation by -5:

\[\frac{{-5y}}{{-5}} = \frac{{-11}}{{-5}}\]

Simplifying, we have:

\(y = \frac{{11}}{{5}}\)

**Step 4:**
Therefore, the solution to the equation is \(y = \frac{{11}}{{5}}\).

In summary, the solution to the equation \(\frac{{-2}}{{5y - 3}} = -\frac{{1}}{{4}}\) is \(y = \frac{{11}}{{5}}\).

Answer is 55/12