We can find MSE.Strain by using the variances to get the SSE.Strain and then dividing by the strain degrees of freedom. Your strain degrees of freedom are $df = 4(8-1) = 28$ since each variance was computed with 7 degrees of freedom. Therefore, MSE.Strain is given by: $$ MSE.Strain = \frac{7\cdot 18+7\cdot 23+7\cdot 21+7\cdot 20}{28} = 20.5 $$

Then for a $t_{df=28}$-distribution, the 0.05 two-tailed critical value is $t^*_{0.025,df=28}$ = qt(0.975, 28) = 2.048.

The LSD statistic is then: $$ LSD = t^*_{0.025,df=28}\sqrt{MSE.Strain\left(\frac{1}{8}+\frac{1}{8}\right)} = 2.048\sqrt{20.5/4} = 4.64. $$

We would reject the hypotheses that any means differing by more than 4.64 are equal. So we reject B being equal to A or D, and C being equal to D.