Can the 2nd generation pencil go to the iPad 8th generation

No.

The 8th generation iPad works with the First generation Apple Pencil.

No - the second generation Apple Pencil is not compatible with iPad8.

All models of iPad with a Lightning Port, that support Apple Pencil, require a first generation Pencil.

Here is the full compatibility list for Apple Pencil and iPad:

Apple Pencil (2nd generation)

You can use Apple Pencil (2nd generation) with these iPad models: 

• iPad Air (4th generation)
• iPad Pro 12.9-inch (3rd generation) and later
• iPad Pro 11-inch (1st generation) and later

Apple Pencil (1st generation)

You can use Apple Pencil (1st generation) with these iPad models:

• iPad (8th generation)
• iPad mini (5th generation)
• iPad (7th generation)
• iPad (6th generation)
• iPad Air (3rd generation)
• iPad Pro 12.9-inch (1st or 2nd generation)
• iPad Pro 10.5-inch
• iPad Pro 9.7-inch

Not sure which iPad you have? Identify your iPad model.

Compatible with

• iPad Air (4th generation)
• iPad Pro 12.9-inch (3rd and 4th generation)
• iPad Pro 11-inch (1st and 2nd generation)

https://www.apple.com/apple-pencil/