Which graph shows Chemical Equilibrium?
Firstly, you need to understand what it means when a system is in equilibrium. Equilibrium is the state of a system where the rate of the forward and reverse reaction are equal. 

Note: this doesn't mean that the reaction completely stops, all this means that the concentration of the reactants and products remain constant. 

A simple example of this can be shown in an experiment where a cube of sugar is placed in a saturated solution of sugar. If you leave it for a few days and come back, you will find that the shape of the sugar cube has changed. Instead of being a smooth, perfect cube, it is a irregular shape. However when if weigh the solid sugar, you find that it will weight exactly the same as the original sugar cube. Now this can be explained by the fact that the solid sugar is in equilibrium with the dissolved sugar in the saturated solution. Despite the forward and reverse reaction being equal (as no more sugar will dissolve) the reaction is still occurring. At a microscopic level, glucose molecules in the sugar cube are dissolving into the solution while dissolved sugar molecules precipitate out onto the sugar cube. However where they precipitate on the cube is random, hence they don't form a perfect cube. This is why the sugar cube changes shape but has the same original mass.

To do this question, it is important that you understand the concept that the reaction still occurs when a system reaches equilibrium. Now, lets look at each graph separately (remember, when we are looking at these graphs, we are only interested at what is happening at the end, what happens at the start is irrelevant):

1: Here the forward and reverse reaction are equal, so from our definition of equilibrium, this graphs shows a system in equilibrium. You should note that despite the system being at equilibrium, the reaction is still going 

2,3: Here in both graphs the forward and reverse reaction are not equal. Therefore the system can't be in equilibrium. This is because in graph 2, the rate of the backward reaction is greater than the rate of the forward reaction. Hence the concentration of the products will be decreasing while the concentration of the reactants will increase. Vice verse for graph 3

4,5,6: Here, since the concentration of the reactants and the products are not changing over time, this means that the forward and reverse reaction is the same. Therefore, the system is in equilibrium

7: In this graph, the concentration of the products is increasing while the concentration of the reactants is decreasing. Hence the forward reaction must be greater than the backward reaction. Therefore, the system isn't in equilibrium.

So to recap the ideas that we heave just learnt, here is the  2 main things to check to work out if a system is in equilibrium or not:


Is the forward and backward reaction equal? if they are equal, this means that the system is in equilibrium. If they aren't equal, the system isn't in equilibrium
Is the concentration of the products and the reactants constant over time? if they are constant, the system is equilibrium. Note, the concentration of the products and reactants don't have to be equal. If concentration of the product and reactants are aren't constant, the system isn't in equilibrium.