How to solve the problem 378x6 using place value with regrouping. explain how you knew to regroup

I can regroup using distributive property

remember a (b+c) = ab+ac

so

(378) (6) = (6) (378) = (6) (300+70+8) =

(6) (300) + (6) (70) + (6) (8) =

1800+420+48=

1000+800+400+20+40+8=

1000+1200+60+8=

1000+1000+200+60+8=

2000+200+60+8=

2268