Define the Variable

Let the number Radha thought of be $x$. The value to be subtracted is $6\frac{3}{5}$, which can be converted to an improper fraction: $6\frac{3}{5} = \frac{6 \times 5 + 3}{5} = \frac{33}{5}$

$\frac{33}{5}$

Set up the Equation

According to the problem, subtracting $\frac{33}{5}$ from $x$ and multiplying by $10$ equals $4x$. This gives the equation: $10 \left( x - \frac{33}{5} \right) = 4x$

$10 \left( x - \frac{33}{5} \right) = 4x$

Solve for x

Distribute the $10$: $10x - 10 \times \frac{33}{5} = 4x$. Simplifying the fraction term: $10x - 66 = 4x$. Subtract $4x$ from both sides and add $66$ to both sides: $6x = 66$. Dividing by $6$: $x = 11$

$x = 11$