Answer: Yes they are equivalent.
Explanation
Let's expand the first expression.
2(4x+3y)+2(x+y)
8x+6y+2x+2y
(8x+2x)+(6y+2y)
10x+8y
Then factor out the GCF 2
2*5x + 2*4y
2(5x+4y)
This proves that 2(4x+3y)+2(x+y) and 2(5x+4y) are equivalent.
