To convert \(-232330_6\) (base 6) to base 4, we will follow these steps:

### Step 1: Convert from base 6 to base 10
The number \(-232330_6\) in base 6 is expanded as follows:

\[
-232330_6 = -(2 \times 6^5 + 3 \times 6^4 + 2 \times 6^3 + 3 \times 6^2 + 3 \times 6^1 + 0 \times 6^0)
\]

Now, let's calculate each term:

\[
2 \times 6^5 = 2 \times 7776 = 15552
\]
\[
3 \times 6^4 = 3 \times 1296 = 3888
\]
\[
2 \times 6^3 = 2 \times 216 = 432
\]
\[
3 \times 6^2 = 3 \times 36 = 108
\]
\[
3 \times 6^1 = 3 \times 6 = 18
\]
\[
0 \times 6^0 = 0
\]

Now, sum them up:

\[
15552 + 3888 + 432 + 108 + 18 = 20000
\]

Thus, \(-232330_6 = -20000_{10}\).

### Step 2: Convert from base 10 to base 4
Next, we need to convert \(-20000_{10}\) to base 4. We repeatedly divide by 4 and record the remainders:

\[
20000 \div 4 = 5000 \ \text{remainder} \ 0
\]
\[
5000 \div 4 = 1250 \ \text{remainder} \ 0
\]
\[
1250 \div 4 = 312 \ \text{remainder} \ 2
\]
\[
312 \div 4 = 78 \ \text{remainder} \ 0
\]
\[
78 \div 4 = 19 \ \text{remainder} \ 2
\]
\[
19 \div 4 = 4 \ \text{remainder} \ 3
\]
\[
4 \div 4 = 1 \ \text{remainder} \ 0
\]
\[
1 \div 4 = 0 \ \text{remainder} \ 1
\]

Reading the remainders from bottom to top, \(-20000_{10}\) in base 4 is \(103203200_4\).

### Final Answer:
\[
-232330_6 = -103203200_4
\]

Would you like more details or have any questions?

Here are 5 related questions for further practice:
1. Convert \( 234520_6 \) to base 4.
2. Convert \( -45321_6 \) to base 8.
3. Convert \( 101101_2 \) to base 6.
4. Convert \( 321032_4 \) to base 6.
5. Convert \( -32110_6 \) to base 5.

**Tip:** When converting between bases, it is often easier to first convert to base 10, then to the desired base.

Learn how to convert -232330 from base 6 to base 4 with a step-by-step explanation. This problem covers key concepts in base conversion and positional notation, and is ideal for students in Grades 9-12.

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