# Neither do people put

"Neither does anyone pour" or "People never put"

# new wine

This refers to wine that has not fermented yet. Alternate translation: "unfermented wine" or "grape juice"  or "unfermented fruit juice"

# old wineskins

This refers to wineskins that have stretched and dried out because they were already used for fermenting wine.

# wineskins

"wine bags" or "skin bags." These were bags made out of animal skins.

# the wine will be spilled, and the wineskins will be destroyed

"and this will ruin the wineskins and spill the wine"

# the skins will burst

When the new wine ferments and expands, old wineskins tear open because they can no longer stretch out.

# fresh wineskins

"new wineskins" or "new wine bags." This refers to wineskins that no one has used.

# both will be preserved

"this will keep safe both the wineskins and the wine"