There question is incomplete:

• There is no variable cost given for manufacturing method B. I'll assume it is b.
• It is unclear as to quantity for which the cost of manufacturing by both methods is the same. I'll assume it is the break-even quantity.

The break even point is when the revenue from sales = cost of manufacture

So the question is asking for what quantity is the cost of manufacture using method A equal to the cost of manufacture using method B.

cost of manufacture = fixed cost + variable cost × quantity

Method A: manufacturing cost = 40,000 + 23 × quantity

Method B: manufacturing cost = 52,000 + b × quantity

→ 40,000 + 23 × quantity = 52,000 + b × quantity

→ 23 × quantity - b × quantity = 52,000 - 40,000

→ quantity(23 - b) = 12,000

→ quantity = 12,000/(23 - b)

I'll let you fill in the value of b; if b has no variable cost, b = 0.