Consider the following expressions:

To determine which operator can be inserted to make the statement true, we will evaluate both sides of the inequality.

Let's simplify the left side:

1. **Calculate the left side**:
\[
6 - 1/4 * 28 - 2 1/4
\]

Start by simplifying \(1/4 * 28\):
\[
1/4 * 28 = 7
\]

Now substitute back into the expression:
\[
6 - 7 - 2 1/4
\]

Convert \(2 1/4\) to an improper fraction:
\[
2 1/4 = \frac{9}{4}
\]

Now we have:
\[
6 - 7 - \frac{9}{4} = -1 - \frac{9}{4} = -1 - 2.25 = -3.25 = -\frac{13}{4}
\]

Thus, the left side simplifies to \(-\frac{13}{4}\).

2. **Calculate the right side**:
\[
3/4 + 4 * 2 - 11
\]

Simplifying \(4 * 2\):
\[
4 * 2 = 8
\]

Now substitute back into the expression:
\[
\frac{3}{4} + 8 - 11
\]

This simplifies to:
\[
\frac{3}{4} + 8 - 11 = \frac{3}{4} + 8 - 11 = \frac{3}{4} - 3 = \frac{3}{4} - \frac{12}{4} = -\frac{9}{4}
\]

So, the right side simplifies to \(-\frac{9}{4}\).

3. **Compare both sides**:
- Left side: \(-\frac{13}{4}\)
- Right side: \(-\frac{9}{4}\)

Now we can evaluate which operator can be valid between these two sides:
- \(-\frac{13}{4} < -\frac{9}{4}\)

Thus, the correct operator to insert is:
\[
<
\]
Therefore, the answer is \(<\).