# But he went out

The word "he" refers to the man Jesus healed.

# began to declare it freely

"began to tell people in many places about what Jesus had done" 

# that Jesus could no longer enter a town openly

"so much that Jesus could no longer enter a town publicly" or "that Jesus could no longer enter the towns in a way that many people would see him" 

# remote places

"lonely places" or "places where no one lived"

# from everywhere

"from all over the region"