There are 6 years (even), so put the origin between 2014 and 2015 and use a half-year unit, $X = -5,-3,-1,1,3,5$, so $\sum X = 0$.

For 2018 the code is $X = 7$, giving $30 + 14 = 44$.

There are $n = 6$ years (even), so there is no middle year. Put the origin midway between 2014 and 2015 and use a half-year unit, giving the consecutive odd codes $X = -5, -3, -1, 1, 3, 5$; then $\sum X = 0$.

Hence

The trend line is $Y_t = 30 + 2X$, where one $X$-unit is half a year. Since one full year equals $2$ units of $X$, the trend rises by $2b = 2 \times 2 =$ Rs 4 lakh per year.

Estimate for 2018. From the origin (mid-2014/2015), the middle of 2018 is $3.5$ years ahead $= 7$ half-year units, so $X = 7$ and $Y_t = 30 + 2(7) = 44$.

Independent check. Positive-side products $31 + 105 + 210 = 346$; negative-side $110 + 69 + 27 = 206$; $\sum XY = 346 - 206 = 140$, matching the table, so $b = 2$. The trend values $20, 24, 28, 32, 36, 40$ (from $X = -5,\ldots,5$) sum to $180 = \sum Y$, confirming the fit.

The consecutive-odd codes $-5, -3, -1, 1, 3, 5$ are what make $\sum X = 0$ for an even number of years; equivalently one can take $X$ in whole years as $-2.5, -1.5, \ldots, 2.5$, but integer half-year codes keep the arithmetic clean.

For an even number of years, wrongly using $X = -3, -2, -1, 0, 1, 2$ (which has $\sum X \ne 0$ and no year at $0$). With six years there is no middle year, so the codes must be the odd numbers $\pm 1, \pm 3, \pm 5$ about a point between the two central years.