The given expression is:

$22 - \left[ 6 - (10 - 4 + 3) \right] \div 2 \times 3$

Let’s solve this step-by-step following the order of operations (PEMDAS/BODMAS):

1. Parentheses (Innermost first):
   Start by solving inside the parentheses: $(10 - 4 + 3) = 9$ Now the expression becomes: $22 - \left[ 6 - 9 \right] \div 2 \times 3$

2. Brackets:
   Simplify the brackets: $6 - 9 = -3$ Now the expression becomes: $22 - (-3) \div 2 \times 3$

3. Division and Multiplication (left to right): First, handle the division: $(-3) \div 2 = -1.5$ Now multiply by 3: $-1.5 \times 3 = -4.5$ Now the expression becomes: $22 - (-4.5)$

4. Final subtraction: Subtracting a negative is the same as adding: $22 + 4.5 = 26.5$

Thus, the value of the expression is 26.5.

Would you like more details on any step, or have further questions?

Here are 5 related questions for practice:

1. Solve: $15 - [8 - (12 - 3)] \div 3 \times 4$
2. Evaluate: $30 - [5 - (20 - 10 + 5)] \times 2$
3. What is the result of: $50 - [7 - (14 - 6)] \div 4 \times 5$
4. Simplify: $18 - [4 - (9 - 2)] \div 2 \times 3$
5. Calculate: $25 - [10 - (15 - 8 + 2)] \div 5 \times 4$

Tip: Always remember the order of operations (PEMDAS/BODMAS) when solving complex expressions. Start with parentheses and work your way out!