Random Puzzles 

Workings

Hint
Fill the 9-litre container first.

Answer
Here are the contents of the containers after each stage:

A = 9 litres, B = 4 litres
A     B
9     0     fill A
5     4     fill B from A (leaving 5 litres in A)
5     0     empty B
1     4     fill B from A (leaving 1 litre in A)
1     0     empty B
0     1     fill B from A
9     1     fill A
6     4     fill B from A (only 3 more litres fit in B)
6     0     empty B

This leaves 6 litres in container A.

Workings

Hint
One answer changes Warm to Worm.

Answer
WARM, WORM, WORK, CORK, COOK, COOL

or

WARM, WORM, WORD, WOOD, WOOL, COOL.

Workings

Hint
Calendar.

Answer
Dragon.

From the Chinese calendar in reverse order.

Workings

Hint
The first letters of the words are: A, P, T, I, P, U, A, R, R, W, D, C, R, B, E.

Answers
----nst = against ----nip = parsnip ----fth = twelfth ----rno = inferno ----dox = paradox ----sil = utensil ----nac = almanac ----iem = requiem ----arb = rhubarb ----ior = warrior ----bey = disobey ----van = caravan ----ipt = receipt ----dth = breadth ----nox = equinox