### Solution:

Given that two years ago, Ram was 3 times older than his daughter and after six years he will be 4 years older than twice her daughter. We need to find the present age of Ram and his daughter.Let the present of Ram and his daughter be x years and y years.

Now, two years ago, Ram was 3 times older than his daughter, therefore, we have,

$\n \n \n \n x\u22122=3(y\u22122)\n \n \n \n \n \u21d2x\u22122=3y\u22126\n \n \n \n \n \u21d2x=3y\u22124\u2009\u2009\u2009...(i)\n \n \n \n \n $

After six years he will be 4 years older than twice her daughter,

$\n \n \n \n x+6=2(y+6)+4\n \n \n \n \n \u21d2x+6=2y+12+4\n \n \n \n \n \u21d2x\u22122y=16\u22126\n \n \n \n \n \u21d2x\u22122y=10\u2009\u2009\u2009...(ii)\n \n \n \n \n $

Now, substituting the value of x from equation (i) in equation (ii),

$\n \n \n \n (3y\u22124)\u22122y=10\n \n \n \n \n \u21d23y\u22124\u22122y=10\n \n \n \n \n \u21d23y\u22122y=10+4\n \n \n \n \n \u21d2y=14\n \n \n \n \n $

Now, substituting the value of y in equation (i), we have,

$\n \n \n \n x=3\n \n 14\n \u22124\n \n \n \n \n \u21d2x=42\u22124\n \n \n \n \n \u21d2x=38\n \n \n \n \n $

Thus, the present age of Ram is 38 years and of his daughter is 14 years.

Therefore, option 4 is correct.