What does that say?

'String' usually refers to something in the form of a curvable line made of something probably thicker than thread, but not as thick as a rope. This usage covers Answers 1 - 3 inclusive (the strings in whole families of instruments such as the violin; string-like party accessories; a series of events where one can 'join up the dots' and identify a pattern of behaviour that may need dealing with).
The version in Answer 4 continues this metaphor, but in the form of a verb.

... Meanwhile, 'spring' as a noun can mean, among other things:
(as in Answer 1) a piece of shaped metal under tension which will store or absorb energy, e.g. within the suspension system of a vehicle;
(Answer 3) The season between winter and summer;
(Answer 4) The source point at which water emerges naturally from the ground.

The obvious meaning of 'face' would be for the front of the head of a person or animal, or also a coin, clock or building (Answer 3) or even a cliff: anything that has an easily identifiable 'front side'. There is then the metaphorical verb usage of 'facing the wall', 'facing (perhaps, uncomfortable) facts' or simply of one turnable thing 'facing' another ('a seat facing the window', 'musicians should check they are facing the conductor').
The usage in Answer 4 is metaphorical and idiomatic, but 'face' is still a noun there; 'face value' in Answer 1 refers to the taking of things by appearances (e.g. a banknote with a 'face value' of £10 may be a forgery; a smart person with a smile may in fact turn out to be sad, or an assassin, or both). 'Face' here is either an adjective (meaning 'on the surface; as seen; by denotation rather than connotation') or perhaps an appositive noun (as in 'face cream'); but certainly not a verb.

The verb 'close' (sounding as though it were spelt with a Z) is the odd one out.
'Close' can be an adverb, meaning much the same as 'near' (Answers 1 & 4), or a small, usually dead-end residential road (Answer 2), presumably because all the houses are nearby to each other ~ and also the far end of the street is shut (like 'closed') rather than leading onward elsewhere.

All these senses are more or less connected by the meaning (literal or figurative) of a machine or situation exerting concentrated pressure; but only in Answer 4 is the word in fact a verb.

'Plant' is only a verb in Answer 3, in the sense of sticking an object into the ground (as with 'a plant' ~ as in Answer 2 ~ but here, the action is metaphorical).
Perhaps somewhat confusingly, 'plant' can also refer to a complete factory ('a car plant' ~ which sounds like something very science-fictional until you've understood it!), or any unspecified number of freestanding machines, e.g. boilers or bulldozers (Answer 4).

'To ring' (Answer 2) means 'to call on the telephone'.
The 'ring' in Answer 1 is a physical shape, presumably more or less circular; the burners on top of a kitchen stove (Answer 4) are also 'rings', while we also refer to a 'ring' of criminals (presumably not so conspicuous or neatly shaped, but with a sense of them 'all being in it together').

You may well wish to investigate this further with the aid of a good English-language dictionary.
You are probably most familiar with 'sound' as a noun (Answer 1) and verb (transitive as in Answer 3, else intransitive as in 'this letter sounds like the name of an insect'); among other duties, it can refer to 'sounding out' people to see what they think (as in 'un sondage' in French), which in turn refers to the deep narrow stretch of sea ~ e.g. Plymouth Sound ~ where sailors need to take regular readings ('soundings') and make sure they are not suddenly in too shallow water for safety.
The correct answer uses 'sound' as an adjective, as in 'safe and sound' (cf. the German 'gesund'); possibly suggesting that something that's healthy will 'sound' (verb!) healthy, for instance, if you tap it.

'Back' in Answer 1 is an adverb describing the direction, in time, that people are being encouraged to think.
In Answer 2 the word is a straightforward noun; its metaphorical meaning appears in the verb in Answer 3 ( = 'to move backwards; to withdraw'), but ~ perhaps confusingly ~ we can also 'back' something when we are supporting it (as in the 'I'm backing Britain' campaign, back [!] in the 1960s, to encourage people to buy British-made products and support the economy, such as the original Mini car).
'Back' in Answer 4 means the rearmost, e.g. the back seat in a bus or cinema. The metaphor here aims to suggest that the new-year plans do not require active attention in the imminent future ~ like putting a pan on to simmer gently at the back of the stove, while you are busier stirring something else nearer to you.

'Tap' is used adjectivally in Answer 2, though it could alternatively be defined as an apposed noun.
Answer 1 refers to the noise made by someone's tapping action (a light, repeated knock, such as the sound of a blind person walking along a familiar street and tapping their white stick every so often to check where they are); similarly ~ perhaps with a small hammer ~ in Answer 3.
'Tapping off' a fluid, or 'tapping into' something (physically or metaphorically) means opening a tap to encourage the good stuff inside to flow out, e.g. molten metal from a furnace, or wisdom or advice from a person or group with previous valuable experience.