Given equilibrium

$$\mathrm{\mathop {C{O_{(g)}} + 3{H_2}(g)}\limits_{(n = 4)}} \rightleftharpoons \mathrm{\mathop {C{H_4}_{(g)} + {H_2}O(g)}\limits_{(n = 4)}}$$

Temperature $\to$ Constant

Pressure $\to$ Increases by two fold.

It is based on Le Chatelier's principle. The principle states that if a change of condition is applied to a system in equilibrium, the system will shift in a direction that relieves the stress.

When pressure increases in a chemical equilibrium, the equilibrium shifts towards the side of the reaction with fewer moles of gas molecules. According to the principle, the reaction will favor the side that provides fewer gas molecules to counteract the increased pressure.

In this equilibrium, fewer gas molecules are on the produce side and on increase in pressure, equilibrium shifts towards products - forwarded reaction occurs. As a result, concentration of the products increases.

4) Concentration of reactants and products increases.

$-$ Correct

With increase in pressure, at constant temperature, the concentration of both reactants and products will increase because the same amount of gas is now in a smaller volume.

(B) Equilibrium will shift in forward direction

Correct

Increase in pressure causes product formation as the equilibrium shift is in the forward direction.

(C) Equilibrium constant increases since concentration of products increases.

Not correct.

The expression for equilibrium constant (K$_c$) for the given equilibrium can be written as

$${K_c} = {{[C{H_4}][{H_2}O]} \over {[CO]{{[{H_2}]}^3}}}$$

Equilibrium constant is not changed with increase in pressure and increase in concentration of reactants or products.

So, the equilibrium constant value is does not affected by change in concentration. If the change increase in concentration of product takes place, the equilibrium position will be shifted to counteract the change. So, equilibrium const value does not increase. Statement is incorrect.

(D) Equilibrium constant remains unchanged as concentration of reactants and products remain same.

State is incorrect.

In the reaction, increase in pressure causes changes in the concentration of rectants and products but the equilibrium constant will not change.

Statements (A) and (B) are correct.