In an adjoining circuit, the equivalent resistance between points A and B is: 

Resistance is the ability of any electrical component to resist electric current across it.

Equivalent Resistance can be defined as the resistance of the resistor which will replace all the resistors between two points and will draw the same current between these two points as it was flowing Earlier.

Ohms Law: At constant temperature, a potential difference is the product of current and resistance.

In the given diagram, the three $2\Omega$ resistors are in parallel with each other.

The Equivalent resistance across them $R^{\text{'}}$ can be represented as
$\frac{1}{R^{\text{'}}}=\frac{1}{2\Omega }+\frac{1}{2\Omega }+\frac{1}{2\Omega }$
$\Rightarrow \frac{1}{R^{\text{'}}}=\frac{3}{2\Omega }$

$\Rightarrow R^{\text{'}}=\frac{2\Omega }{3}$

$R^{\text{'}}=0.67\Omega$
Now, this combination is in series with a 40 resistor.
So, Equivalent resistance
$R=R^{\text{'}}+4\Omega =0.67\Omega +4\Omega =4.67\Omega$
So, 3 is the correct option.